fisica para biologia f107 a - um blog do instituto de

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FISICA PARA BIOLOGIA F107 A : AULA 10 PROFESSOR Orlando Luis Goulart Peres Pagina do curso: https://sites.ifi.unicamp.br/orlando/ensino/f-107-fisica-para-biologia/ Moodle: https://www.ggte.unicamp.br/ea/

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Page 1: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

FISICA PARA BIOLOGIA F107 A : AULA 10

PROFESSOR Orlando Luis Goulart Peres

Pagina do curso: https://sites.ifi.unicamp.br/orlando/ensino/f-107-fisica-para-biologia/Moodle: https://www.ggte.unicamp.br/ea/

Page 2: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

A NATUREZA ONDULATORIA DA MATERIA

Do experimento Compton e fotoelétrico a luz parece se comportar como uma partícula.

Louis de Broglie propôs por similaridade que partículas poderiam ter comportamento de ondas.

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p=mv onde m massa da partícula e v a velocidade

Page 3: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

COMPRIMENTO DE ONDA ELETTROMAGNETICA

Page 4: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

MODELOS DO ATOMO: RUTHERFORD

Rutherford: o átomo não esta espalhado: vazios

Page 5: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

ESPECTRO ATOMICO: O QUE VEMOS?

Espectro acima: hidrogênio

Espectro meio: helio

Page 6: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

SERIE DE BALMER

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sha1_base64="nmDil0ue14jwyWYHIx/Cn5lx3a8=">AAACB3icbZDLSgMxGIX/8Vpr1erWTbAICloSEaoLQXDjsoq9QG9k0rQNTWaGJCOUYZ7Bja/ixoUivoE738b0stDWA4GPcxL+/MePpDAW429vaXlldW09s5HdzG1t7+R3c1UTxprxCgtlqOs+NVyKgFessJLXI82p8iWv+cObcV575NqIMHiwo4i3FO0HoicYtc7q5I+TplboPr0iJ/iydI6aVihuEMHtpJSiSajSdnJK0k6+gIt4IrQIZAYFmKncyX81uyGLFQ8sk9SYBsGRbSVUW8EkT7PN2PCIsiHt84bDgLrBrWSyUooOndNFvVC7E1g0cX+/SKgyZqR8d1NROzDz2dj8L2vEtnfRSkQQxZYHbDqoF0tkQzTuB3WF5szKkQPKtHB/RWxANWXWtZh1JZD5lRehelYkuEjuMGRgHw7gCAiU4BpuoQwVYPAEL/AG796z9+p9TOta8ma97cEfeZ8//U2aGw==</latexit><latexit sha1_base64="B8H8r/Py7twED27/7ELoLtkV4zA=">AAACEnicbVDLSgMxFM3UV62vqks3wSIoaElEqApCwY3LKvYBnbZk0rQNTWaGJCOUYb7Bjb/ixoUibl25829M21lo64ELh3Pu5d57vFBwbRD6djILi0vLK9nV3Nr6xuZWfnunpoNIUValgQhUwyOaCe6zquFGsEaoGJGeYHVveD326w9MaR7492YUspYkfZ/3OCXGSp38UewqCe+SK3yMLkpn0DVcMg0xaselBE5MmbTjE5x08gVURBPAeYJTUgApKp38l9sNaCSZb6ggWjcxCk0rJspwKliScyPNQkKHpM+alvrELm7Fk5cSeGCVLuwFypZv4ET9PRETqfVIerZTEjPQs95Y/M9rRqZ33oq5H0aG+XS6qBcJaAI4zgd2uWLUiJElhCpub4V0QBShxqaYsyHg2ZfnSe20iFER36JC+TKNIwv2wD44BBiUQBncgAqoAgoewTN4BW/Ok/PivDsf09aMk87sgj9wPn8Ap4KbjA==</latexit><latexit sha1_base64="sDYEGJxkLO+wMlfoKW2xn89S3wA=">AAACEnicbVDLSgMxFM3UV62vUZdugkVQ0DKRQlUQCm5cVrEP6ItMmrahSWZIMkIZ5hvc+CtuXCji1pU7/8Z02oVWD1w4nHMv997jh5xp43lfTmZhcWl5JbuaW1vf2Nxyt3dqOogUoVUS8EA1fKwpZ5JWDTOcNkJFsfA5rfujq4lfv6dKs0DemXFI2wIPJOszgo2Vuu5R3FIC3iaX6Ng7LxVhyzBBNUReJy4lMDVF0olPUNJ1817BSwH/EjQjeTBDpet+tnoBiQSVhnCsdRN5oWnHWBlGOE1yrUjTEJMRHtCmpRLbxe04fSmBB1bpwX6gbEkDU/XnRIyF1mPh206BzVDPexPxP68Zmf5ZO2YyjAyVZLqoH3FoAjjJB/aYosTwsSWYKGZvhWSIFSbGppizIaD5l/+S2mkBeQV0U8yXL2ZxZMEe2AeHAIESKINrUAFVQMADeAIv4NV5dJ6dN+d92ppxZjO74Becj2+owpuQ</latexit><latexit sha1_base64="sDYEGJxkLO+wMlfoKW2xn89S3wA=">AAACEnicbVDLSgMxFM3UV62vUZdugkVQ0DKRQlUQCm5cVrEP6ItMmrahSWZIMkIZ5hvc+CtuXCji1pU7/8Z02oVWD1w4nHMv997jh5xp43lfTmZhcWl5JbuaW1vf2Nxyt3dqOogUoVUS8EA1fKwpZ5JWDTOcNkJFsfA5rfujq4lfv6dKs0DemXFI2wIPJOszgo2Vuu5R3FIC3iaX6Ng7LxVhyzBBNUReJy4lMDVF0olPUNJ1817BSwH/EjQjeTBDpet+tnoBiQSVhnCsdRN5oWnHWBlGOE1yrUjTEJMRHtCmpRLbxe04fSmBB1bpwX6gbEkDU/XnRIyF1mPh206BzVDPexPxP68Zmf5ZO2YyjAyVZLqoH3FoAjjJB/aYosTwsSWYKGZvhWSIFSbGppizIaD5l/+S2mkBeQV0U8yXL2ZxZMEe2AeHAIESKINrUAFVQMADeAIv4NV5dJ6dN+d92ppxZjO74Becj2+owpuQ</latexit><latexit sha1_base64="sDYEGJxkLO+wMlfoKW2xn89S3wA=">AAACEnicbVDLSgMxFM3UV62vUZdugkVQ0DKRQlUQCm5cVrEP6ItMmrahSWZIMkIZ5hvc+CtuXCji1pU7/8Z02oVWD1w4nHMv997jh5xp43lfTmZhcWl5JbuaW1vf2Nxyt3dqOogUoVUS8EA1fKwpZ5JWDTOcNkJFsfA5rfujq4lfv6dKs0DemXFI2wIPJOszgo2Vuu5R3FIC3iaX6Ng7LxVhyzBBNUReJy4lMDVF0olPUNJ1817BSwH/EjQjeTBDpet+tnoBiQSVhnCsdRN5oWnHWBlGOE1yrUjTEJMRHtCmpRLbxe04fSmBB1bpwX6gbEkDU/XnRIyF1mPh206BzVDPexPxP68Zmf5ZO2YyjAyVZLqoH3FoAjjJB/aYosTwsSWYKGZvhWSIFSbGppizIaD5l/+S2mkBeQV0U8yXL2ZxZMEe2AeHAIESKINrUAFVQMADeAIv4NV5dJ6dN+d92ppxZjO74Becj2+owpuQ</latexit><latexit sha1_base64="sDYEGJxkLO+wMlfoKW2xn89S3wA=">AAACEnicbVDLSgMxFM3UV62vUZdugkVQ0DKRQlUQCm5cVrEP6ItMmrahSWZIMkIZ5hvc+CtuXCji1pU7/8Z02oVWD1w4nHMv997jh5xp43lfTmZhcWl5JbuaW1vf2Nxyt3dqOogUoVUS8EA1fKwpZ5JWDTOcNkJFsfA5rfujq4lfv6dKs0DemXFI2wIPJOszgo2Vuu5R3FIC3iaX6Ng7LxVhyzBBNUReJy4lMDVF0olPUNJ1817BSwH/EjQjeTBDpet+tnoBiQSVhnCsdRN5oWnHWBlGOE1yrUjTEJMRHtCmpRLbxe04fSmBB1bpwX6gbEkDU/XnRIyF1mPh206BzVDPexPxP68Zmf5ZO2YyjAyVZLqoH3FoAjjJB/aYosTwsSWYKGZvhWSIFSbGppizIaD5l/+S2mkBeQV0U8yXL2ZxZMEe2AeHAIESKINrUAFVQMADeAIv4NV5dJ6dN+d92ppxZjO74Becj2+owpuQ</latexit><latexit sha1_base64="sDYEGJxkLO+wMlfoKW2xn89S3wA=">AAACEnicbVDLSgMxFM3UV62vUZdugkVQ0DKRQlUQCm5cVrEP6ItMmrahSWZIMkIZ5hvc+CtuXCji1pU7/8Z02oVWD1w4nHMv997jh5xp43lfTmZhcWl5JbuaW1vf2Nxyt3dqOogUoVUS8EA1fKwpZ5JWDTOcNkJFsfA5rfujq4lfv6dKs0DemXFI2wIPJOszgo2Vuu5R3FIC3iaX6Ng7LxVhyzBBNUReJy4lMDVF0olPUNJ1817BSwH/EjQjeTBDpet+tnoBiQSVhnCsdRN5oWnHWBlGOE1yrUjTEJMRHtCmpRLbxe04fSmBB1bpwX6gbEkDU/XnRIyF1mPh206BzVDPexPxP68Zmf5ZO2YyjAyVZLqoH3FoAjjJB/aYosTwsSWYKGZvhWSIFSbGppizIaD5l/+S2mkBeQV0U8yXL2ZxZMEe2AeHAIESKINrUAFVQMADeAIv4NV5dJ6dN+d92ppxZjO74Becj2+owpuQ</latexit><latexit sha1_base64="sDYEGJxkLO+wMlfoKW2xn89S3wA=">AAACEnicbVDLSgMxFM3UV62vUZdugkVQ0DKRQlUQCm5cVrEP6ItMmrahSWZIMkIZ5hvc+CtuXCji1pU7/8Z02oVWD1w4nHMv997jh5xp43lfTmZhcWl5JbuaW1vf2Nxyt3dqOogUoVUS8EA1fKwpZ5JWDTOcNkJFsfA5rfujq4lfv6dKs0DemXFI2wIPJOszgo2Vuu5R3FIC3iaX6Ng7LxVhyzBBNUReJy4lMDVF0olPUNJ1817BSwH/EjQjeTBDpet+tnoBiQSVhnCsdRN5oWnHWBlGOE1yrUjTEJMRHtCmpRLbxe04fSmBB1bpwX6gbEkDU/XnRIyF1mPh206BzVDPexPxP68Zmf5ZO2YyjAyVZLqoH3FoAjjJB/aYosTwsSWYKGZvhWSIFSbGppizIaD5l/+S2mkBeQV0U8yXL2ZxZMEe2AeHAIESKINrUAFVQMADeAIv4NV5dJ6dN+d92ppxZjO74Becj2+owpuQ</latexit>

n=1,2,3,..

Page 7: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

LYMAN SERIES

Page 8: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

MODELO DE BOHR

hf = Ea � El<latexit sha1_base64="AYPUDs/SpXR3OlpjZTIn8wU5dd8=">AAAB83icbVBNS8NAEJ34WetX1aOXxSJ4sSQiKIJQkILHCvYD2hA22027dLMJuxOhlP4NLx4U8eqf8ea/cdvmoK0PBh7vzTAzL0ylMOi6387K6tr6xmZhq7i9s7u3Xzo4bJok04w3WCIT3Q6p4VIo3kCBkrdTzWkcSt4Kh3dTv/XEtRGJesRRyv2Y9pWIBKNope6ARLekFtDzWiCDUtmtuDOQZeLlpAw56kHpq9tLWBZzhUxSYzqem6I/phoFk3xS7GaGp5QNaZ93LFU05sYfz26ekFOr9EiUaFsKyUz9PTGmsTGjOLSdMcWBWfSm4n9eJ8Po2h8LlWbIFZsvijJJMCHTAEhPaM5QjiyhTAt7K2EDqilDG1PRhuAtvrxMmhcVz614D5fl6k0eRwGO4QTOwIMrqMI91KEBDFJ4hld4czLnxXl3PuatK04+cwR/4Hz+ADjLkHc=</latexit><latexit sha1_base64="AYPUDs/SpXR3OlpjZTIn8wU5dd8=">AAAB83icbVBNS8NAEJ34WetX1aOXxSJ4sSQiKIJQkILHCvYD2hA22027dLMJuxOhlP4NLx4U8eqf8ea/cdvmoK0PBh7vzTAzL0ylMOi6387K6tr6xmZhq7i9s7u3Xzo4bJok04w3WCIT3Q6p4VIo3kCBkrdTzWkcSt4Kh3dTv/XEtRGJesRRyv2Y9pWIBKNope6ARLekFtDzWiCDUtmtuDOQZeLlpAw56kHpq9tLWBZzhUxSYzqem6I/phoFk3xS7GaGp5QNaZ93LFU05sYfz26ekFOr9EiUaFsKyUz9PTGmsTGjOLSdMcWBWfSm4n9eJ8Po2h8LlWbIFZsvijJJMCHTAEhPaM5QjiyhTAt7K2EDqilDG1PRhuAtvrxMmhcVz614D5fl6k0eRwGO4QTOwIMrqMI91KEBDFJ4hld4czLnxXl3PuatK04+cwR/4Hz+ADjLkHc=</latexit><latexit sha1_base64="AYPUDs/SpXR3OlpjZTIn8wU5dd8=">AAAB83icbVBNS8NAEJ34WetX1aOXxSJ4sSQiKIJQkILHCvYD2hA22027dLMJuxOhlP4NLx4U8eqf8ea/cdvmoK0PBh7vzTAzL0ylMOi6387K6tr6xmZhq7i9s7u3Xzo4bJok04w3WCIT3Q6p4VIo3kCBkrdTzWkcSt4Kh3dTv/XEtRGJesRRyv2Y9pWIBKNope6ARLekFtDzWiCDUtmtuDOQZeLlpAw56kHpq9tLWBZzhUxSYzqem6I/phoFk3xS7GaGp5QNaZ93LFU05sYfz26ekFOr9EiUaFsKyUz9PTGmsTGjOLSdMcWBWfSm4n9eJ8Po2h8LlWbIFZsvijJJMCHTAEhPaM5QjiyhTAt7K2EDqilDG1PRhuAtvrxMmhcVz614D5fl6k0eRwGO4QTOwIMrqMI91KEBDFJ4hld4czLnxXl3PuatK04+cwR/4Hz+ADjLkHc=</latexit><latexit sha1_base64="AYPUDs/SpXR3OlpjZTIn8wU5dd8=">AAAB83icbVBNS8NAEJ34WetX1aOXxSJ4sSQiKIJQkILHCvYD2hA22027dLMJuxOhlP4NLx4U8eqf8ea/cdvmoK0PBh7vzTAzL0ylMOi6387K6tr6xmZhq7i9s7u3Xzo4bJok04w3WCIT3Q6p4VIo3kCBkrdTzWkcSt4Kh3dTv/XEtRGJesRRyv2Y9pWIBKNope6ARLekFtDzWiCDUtmtuDOQZeLlpAw56kHpq9tLWBZzhUxSYzqem6I/phoFk3xS7GaGp5QNaZ93LFU05sYfz26ekFOr9EiUaFsKyUz9PTGmsTGjOLSdMcWBWfSm4n9eJ8Po2h8LlWbIFZsvijJJMCHTAEhPaM5QjiyhTAt7K2EDqilDG1PRhuAtvrxMmhcVz614D5fl6k0eRwGO4QTOwIMrqMI91KEBDFJ4hld4czLnxXl3PuatK04+cwR/4Hz+ADjLkHc=</latexit>

So existe emissão de luz se a tiver a freqüência dada por esta equação.

Page 9: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

MODELO DE BOHR

� =

h

mvperimetro = 2⇡ra = n�

<latexit sha1_base64="xZ5OSRXIwY2FsJPgqc+rEwmafo0=">AAACKXicbVDLSgMxFM34tr6qLt0Ei+CqzIigCIWCG5cKVoVOKXcyd2wwyYxJplCG+R03/oobBUXd+iOmdRa+DgQO55zLzT1RJrixvv/mTU3PzM7NLyzWlpZXVtfq6xsXJs01ww5LRaqvIjAouMKO5VbgVaYRZCTwMro5HvuXQ9SGp+rcjjLsSbhWPOEMrJP69XYoXDiGVphoYMWgLCQdljS8zSGmtAi1pBlqLtHqtKStvTDjVPehRVU12K83/KY/Af1Lgoo0SIXTfv0pjFOWS1SWCTCmG/iZ7RWgLWcCy1qYG8yA3cA1dh1VINH0ismlJd1xSkyTVLunLJ2o3ycKkMaMZOSSEuzA/PbG4n9eN7fJYa/gKsstKva1KMkFtSkd10ZjrpFZMXIEmObur5QNwFVmXbk1V0Lw++S/5GKvGfjN4Gy/0T6q6lggW2Sb7JKAHJA2OSGnpEMYuSMP5Jm8ePfeo/fqvX9Fp7xqZpP8gPfxCVuLpp8=</latexit><latexit sha1_base64="xZ5OSRXIwY2FsJPgqc+rEwmafo0=">AAACKXicbVDLSgMxFM34tr6qLt0Ei+CqzIigCIWCG5cKVoVOKXcyd2wwyYxJplCG+R03/oobBUXd+iOmdRa+DgQO55zLzT1RJrixvv/mTU3PzM7NLyzWlpZXVtfq6xsXJs01ww5LRaqvIjAouMKO5VbgVaYRZCTwMro5HvuXQ9SGp+rcjjLsSbhWPOEMrJP69XYoXDiGVphoYMWgLCQdljS8zSGmtAi1pBlqLtHqtKStvTDjVPehRVU12K83/KY/Af1Lgoo0SIXTfv0pjFOWS1SWCTCmG/iZ7RWgLWcCy1qYG8yA3cA1dh1VINH0ismlJd1xSkyTVLunLJ2o3ycKkMaMZOSSEuzA/PbG4n9eN7fJYa/gKsstKva1KMkFtSkd10ZjrpFZMXIEmObur5QNwFVmXbk1V0Lw++S/5GKvGfjN4Gy/0T6q6lggW2Sb7JKAHJA2OSGnpEMYuSMP5Jm8ePfeo/fqvX9Fp7xqZpP8gPfxCVuLpp8=</latexit><latexit sha1_base64="xZ5OSRXIwY2FsJPgqc+rEwmafo0=">AAACKXicbVDLSgMxFM34tr6qLt0Ei+CqzIigCIWCG5cKVoVOKXcyd2wwyYxJplCG+R03/oobBUXd+iOmdRa+DgQO55zLzT1RJrixvv/mTU3PzM7NLyzWlpZXVtfq6xsXJs01ww5LRaqvIjAouMKO5VbgVaYRZCTwMro5HvuXQ9SGp+rcjjLsSbhWPOEMrJP69XYoXDiGVphoYMWgLCQdljS8zSGmtAi1pBlqLtHqtKStvTDjVPehRVU12K83/KY/Af1Lgoo0SIXTfv0pjFOWS1SWCTCmG/iZ7RWgLWcCy1qYG8yA3cA1dh1VINH0ismlJd1xSkyTVLunLJ2o3ycKkMaMZOSSEuzA/PbG4n9eN7fJYa/gKsstKva1KMkFtSkd10ZjrpFZMXIEmObur5QNwFVmXbk1V0Lw++S/5GKvGfjN4Gy/0T6q6lggW2Sb7JKAHJA2OSGnpEMYuSMP5Jm8ePfeo/fqvX9Fp7xqZpP8gPfxCVuLpp8=</latexit><latexit sha1_base64="xZ5OSRXIwY2FsJPgqc+rEwmafo0=">AAACKXicbVDLSgMxFM34tr6qLt0Ei+CqzIigCIWCG5cKVoVOKXcyd2wwyYxJplCG+R03/oobBUXd+iOmdRa+DgQO55zLzT1RJrixvv/mTU3PzM7NLyzWlpZXVtfq6xsXJs01ww5LRaqvIjAouMKO5VbgVaYRZCTwMro5HvuXQ9SGp+rcjjLsSbhWPOEMrJP69XYoXDiGVphoYMWgLCQdljS8zSGmtAi1pBlqLtHqtKStvTDjVPehRVU12K83/KY/Af1Lgoo0SIXTfv0pjFOWS1SWCTCmG/iZ7RWgLWcCy1qYG8yA3cA1dh1VINH0ismlJd1xSkyTVLunLJ2o3ycKkMaMZOSSEuzA/PbG4n9eN7fJYa/gKsstKva1KMkFtSkd10ZjrpFZMXIEmObur5QNwFVmXbk1V0Lw++S/5GKvGfjN4Gy/0T6q6lggW2Sb7JKAHJA2OSGnpEMYuSMP5Jm8ePfeo/fqvX9Fp7xqZpP8gPfxCVuLpp8=</latexit>

Page 10: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

QUANTIZAÇÃO A LA BOHR

� =

h

mvperimetro = 2⇡ra = n�

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Os electrons ficam em apenas algumas orbitas.

Se ra =n�

eletron

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então � =h

mv=

2⇡ran

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sha1_base64="C3kILPTlhA7FON4Xoar9Oov9hUY=">AAACEnicbVDNS8MwHE3n15xfVY9egkPQy2iHoJfB0IvHCe4D1lLSLN3CkrQk6WCU/g1e/Fe8eFDEqydv/jdmWw+6+SDw8t77kfxemDCqtON8W6W19Y3NrfJ2ZWd3b//APjzqqDiVmLRxzGLZC5EijArS1lQz0kskQTxkpBuOb2d+d0KkorF40NOE+BwNBY0oRtpIgX3hMRMeoIYXSYSzUZ5xOMkbcHGtewmFMkB5JvLArjo1Zw64StyCVEGBVmB/eYMYp5wIjRlSqu86ifYzJDXFjOQVL1UkQXiMhqRvqECcKD+br5TDM6MMYBRLc4SGc/X3RIa4UlMemiRHeqSWvZn4n9dPdXTtZ1QkqSYCLx6KUgZ1DGf9wAGVBGs2NQRhSc1fIR4hU4Y2LVZMCe7yyqukU6+5Ts29v6w2b4o6yuAEnIJz4IIr0AR3oAXaAINH8AxewZv1ZL1Y79bHIlqyiplj8AfW5w+DX53+</latexit>

Reescrevendo

nh = 2⇡ (ramv)<latexit sha1_base64="OqzXYRFt8/ihfGOtPNNl/Z5zfWc=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARKkhJiqAboejGZQX7gCaEyXTSDp2ZhJlJocQu/BU3LhRx62+482+ctllo64ELh3Pu5d57woRRpR3n2yqsrK6tbxQ3S1vbO7t79v5BS8WpxKSJYxbLTogUYVSQpqaakU4iCeIhI+1weDv12yMiFY3Fgx4nxOeoL2hEMdJGCuwjAQfwGta8hHrnsAJlgCAfnQV22ak6M8Bl4uakDHI0AvvL68U45URozJBSXddJtJ8hqSlmZFLyUkUShIeoT7qGCsSJ8rPZ/RN4apQejGJpSmg4U39PZIgrNeah6eRID9SiNxX/87qpjq78jIok1UTg+aIoZVDHcBoG7FFJsGZjQxCW1NwK8QBJhLWJrGRCcBdfXiatWtV1qu79Rbl+k8dRBMfgBFSACy5BHdyBBmgCDB7BM3gFb9aT9WK9Wx/z1oKVzxyCP7A+fwBFZpOv</latexit><latexit sha1_base64="OqzXYRFt8/ihfGOtPNNl/Z5zfWc=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARKkhJiqAboejGZQX7gCaEyXTSDp2ZhJlJocQu/BU3LhRx62+482+ctllo64ELh3Pu5d57woRRpR3n2yqsrK6tbxQ3S1vbO7t79v5BS8WpxKSJYxbLTogUYVSQpqaakU4iCeIhI+1weDv12yMiFY3Fgx4nxOeoL2hEMdJGCuwjAQfwGta8hHrnsAJlgCAfnQV22ak6M8Bl4uakDHI0AvvL68U45URozJBSXddJtJ8hqSlmZFLyUkUShIeoT7qGCsSJ8rPZ/RN4apQejGJpSmg4U39PZIgrNeah6eRID9SiNxX/87qpjq78jIok1UTg+aIoZVDHcBoG7FFJsGZjQxCW1NwK8QBJhLWJrGRCcBdfXiatWtV1qu79Rbl+k8dRBMfgBFSACy5BHdyBBmgCDB7BM3gFb9aT9WK9Wx/z1oKVzxyCP7A+fwBFZpOv</latexit><latexit sha1_base64="OqzXYRFt8/ihfGOtPNNl/Z5zfWc=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARKkhJiqAboejGZQX7gCaEyXTSDp2ZhJlJocQu/BU3LhRx62+482+ctllo64ELh3Pu5d57woRRpR3n2yqsrK6tbxQ3S1vbO7t79v5BS8WpxKSJYxbLTogUYVSQpqaakU4iCeIhI+1weDv12yMiFY3Fgx4nxOeoL2hEMdJGCuwjAQfwGta8hHrnsAJlgCAfnQV22ak6M8Bl4uakDHI0AvvL68U45URozJBSXddJtJ8hqSlmZFLyUkUShIeoT7qGCsSJ8rPZ/RN4apQejGJpSmg4U39PZIgrNeah6eRID9SiNxX/87qpjq78jIok1UTg+aIoZVDHcBoG7FFJsGZjQxCW1NwK8QBJhLWJrGRCcBdfXiatWtV1qu79Rbl+k8dRBMfgBFSACy5BHdyBBmgCDB7BM3gFb9aT9WK9Wx/z1oKVzxyCP7A+fwBFZpOv</latexit><latexit sha1_base64="OqzXYRFt8/ihfGOtPNNl/Z5zfWc=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARKkhJiqAboejGZQX7gCaEyXTSDp2ZhJlJocQu/BU3LhRx62+482+ctllo64ELh3Pu5d57woRRpR3n2yqsrK6tbxQ3S1vbO7t79v5BS8WpxKSJYxbLTogUYVSQpqaakU4iCeIhI+1weDv12yMiFY3Fgx4nxOeoL2hEMdJGCuwjAQfwGta8hHrnsAJlgCAfnQV22ak6M8Bl4uakDHI0AvvL68U45URozJBSXddJtJ8hqSlmZFLyUkUShIeoT7qGCsSJ8rPZ/RN4apQejGJpSmg4U39PZIgrNeah6eRID9SiNxX/87qpjq78jIok1UTg+aIoZVDHcBoG7FFJsGZjQxCW1NwK8QBJhLWJrGRCcBdfXiatWtV1qu79Rbl+k8dRBMfgBFSACy5BHdyBBmgCDB7BM3gFb9aT9WK9Wx/z1oKVzxyCP7A+fwBFZpOv</latexit>

Então se o raio é constante a velocidade também é .

Page 11: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

QUANTIZAÇÃO A LA BOHR II

A condição de raio constante se pode escrever

rn = n2r1<latexit sha1_base64="rInyazYbGl0AGgQj8CUe6j6STDo=">AAAB83icbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoBeh6MVjBfsBbQyb7aZdutmE3YlQSv+GFw+KePXPePPfuG1z0NYHA4/3ZpiZF6ZSGHTdb6ewtr6xuVXcLu3s7u0flA+PWibJNONNlshEd0JquBSKN1Gg5J1UcxqHkrfD0e3Mbz9xbUSiHnCccj+mAyUiwShaqacDdU3UY43owAvKFbfqzkFWiZeTCuRoBOWvXj9hWcwVMkmN6Xpuiv6EahRM8mmplxmeUjaiA961VNGYG38yv3lKzqzSJ1GibSkkc/X3xITGxozj0HbGFIdm2ZuJ/3ndDKMrfyJUmiFXbLEoyiTBhMwCIH2hOUM5toQyLeythA2ppgxtTCUbgrf88ipp1aqeW/XuLyr1mzyOIpzAKZyDB5dQhztoQBMYpPAMr/DmZM6L8+58LFoLTj5zDH/gfP4AhgOQrg==</latexit><latexit sha1_base64="rInyazYbGl0AGgQj8CUe6j6STDo=">AAAB83icbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoBeh6MVjBfsBbQyb7aZdutmE3YlQSv+GFw+KePXPePPfuG1z0NYHA4/3ZpiZF6ZSGHTdb6ewtr6xuVXcLu3s7u0flA+PWibJNONNlshEd0JquBSKN1Gg5J1UcxqHkrfD0e3Mbz9xbUSiHnCccj+mAyUiwShaqacDdU3UY43owAvKFbfqzkFWiZeTCuRoBOWvXj9hWcwVMkmN6Xpuiv6EahRM8mmplxmeUjaiA961VNGYG38yv3lKzqzSJ1GibSkkc/X3xITGxozj0HbGFIdm2ZuJ/3ndDKMrfyJUmiFXbLEoyiTBhMwCIH2hOUM5toQyLeythA2ppgxtTCUbgrf88ipp1aqeW/XuLyr1mzyOIpzAKZyDB5dQhztoQBMYpPAMr/DmZM6L8+58LFoLTj5zDH/gfP4AhgOQrg==</latexit><latexit sha1_base64="rInyazYbGl0AGgQj8CUe6j6STDo=">AAAB83icbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoBeh6MVjBfsBbQyb7aZdutmE3YlQSv+GFw+KePXPePPfuG1z0NYHA4/3ZpiZF6ZSGHTdb6ewtr6xuVXcLu3s7u0flA+PWibJNONNlshEd0JquBSKN1Gg5J1UcxqHkrfD0e3Mbz9xbUSiHnCccj+mAyUiwShaqacDdU3UY43owAvKFbfqzkFWiZeTCuRoBOWvXj9hWcwVMkmN6Xpuiv6EahRM8mmplxmeUjaiA961VNGYG38yv3lKzqzSJ1GibSkkc/X3xITGxozj0HbGFIdm2ZuJ/3ndDKMrfyJUmiFXbLEoyiTBhMwCIH2hOUM5toQyLeythA2ppgxtTCUbgrf88ipp1aqeW/XuLyr1mzyOIpzAKZyDB5dQhztoQBMYpPAMr/DmZM6L8+58LFoLTj5zDH/gfP4AhgOQrg==</latexit><latexit sha1_base64="rInyazYbGl0AGgQj8CUe6j6STDo=">AAAB83icbVBNS8NAEJ3Ur1q/qh69LBbBU0mKoBeh6MVjBfsBbQyb7aZdutmE3YlQSv+GFw+KePXPePPfuG1z0NYHA4/3ZpiZF6ZSGHTdb6ewtr6xuVXcLu3s7u0flA+PWibJNONNlshEd0JquBSKN1Gg5J1UcxqHkrfD0e3Mbz9xbUSiHnCccj+mAyUiwShaqacDdU3UY43owAvKFbfqzkFWiZeTCuRoBOWvXj9hWcwVMkmN6Xpuiv6EahRM8mmplxmeUjaiA961VNGYG38yv3lKzqzSJ1GibSkkc/X3xITGxozj0HbGFIdm2ZuJ/3ndDKMrfyJUmiFXbLEoyiTBhMwCIH2hOUM5toQyLeythA2ppgxtTCUbgrf88ipp1aqeW/XuLyr1mzyOIpzAKZyDB5dQhztoQBMYpPAMr/DmZM6L8+58LFoLTj5zDH/gfP4AhgOQrg==</latexit>

onde r1 = 0, 5⇥ 10�10 m<latexit sha1_base64="xE+HyrM0hByfFs3/ZqepnKJFRUQ=">AAACCnicbVDLSgMxFM3UV62vUZduokVwUUsiim6EohuXFewDOmPJpGkbmswMSUYow6zd+CtuXCji1i9w59+YPhbaeuDC4Zx7ufeeIBZcG4S+ndzC4tLySn61sLa+sbnlbu/UdZQoymo0EpFqBkQzwUNWM9wI1owVIzIQrBEMrkd+44EpzaPwzgxj5kvSC3mXU2Ks1Hb3VRtfotIZ9AyXTEOM7tNjjDKvBFNPSSiztltEZTQGnCd4Sopgimrb/fI6EU0kCw0VROsWRrHxU6IMp4JlBS/RLCZ0QHqsZWlI7F4/Hb+SwUOrdGA3UrZCA8fq74mUSK2HMrCdkpi+nvVG4n9eKzHdCz/lYZwYFtLJom4ioIngKBfY4YpRI4aWEKq4vRXSPlGEGptewYaAZ1+eJ/WTMkZlfHtarFxN48iDPXAAjgAG56ACbkAV1AAFj+AZvII358l5cd6dj0lrzpnO7II/cD5/AGmrmDA=</latexit><latexit sha1_base64="xE+HyrM0hByfFs3/ZqepnKJFRUQ=">AAACCnicbVDLSgMxFM3UV62vUZduokVwUUsiim6EohuXFewDOmPJpGkbmswMSUYow6zd+CtuXCji1i9w59+YPhbaeuDC4Zx7ufeeIBZcG4S+ndzC4tLySn61sLa+sbnlbu/UdZQoymo0EpFqBkQzwUNWM9wI1owVIzIQrBEMrkd+44EpzaPwzgxj5kvSC3mXU2Ks1Hb3VRtfotIZ9AyXTEOM7tNjjDKvBFNPSSiztltEZTQGnCd4Sopgimrb/fI6EU0kCw0VROsWRrHxU6IMp4JlBS/RLCZ0QHqsZWlI7F4/Hb+SwUOrdGA3UrZCA8fq74mUSK2HMrCdkpi+nvVG4n9eKzHdCz/lYZwYFtLJom4ioIngKBfY4YpRI4aWEKq4vRXSPlGEGptewYaAZ1+eJ/WTMkZlfHtarFxN48iDPXAAjgAG56ACbkAV1AAFj+AZvII358l5cd6dj0lrzpnO7II/cD5/AGmrmDA=</latexit><latexit sha1_base64="xE+HyrM0hByfFs3/ZqepnKJFRUQ=">AAACCnicbVDLSgMxFM3UV62vUZduokVwUUsiim6EohuXFewDOmPJpGkbmswMSUYow6zd+CtuXCji1i9w59+YPhbaeuDC4Zx7ufeeIBZcG4S+ndzC4tLySn61sLa+sbnlbu/UdZQoymo0EpFqBkQzwUNWM9wI1owVIzIQrBEMrkd+44EpzaPwzgxj5kvSC3mXU2Ks1Hb3VRtfotIZ9AyXTEOM7tNjjDKvBFNPSSiztltEZTQGnCd4Sopgimrb/fI6EU0kCw0VROsWRrHxU6IMp4JlBS/RLCZ0QHqsZWlI7F4/Hb+SwUOrdGA3UrZCA8fq74mUSK2HMrCdkpi+nvVG4n9eKzHdCz/lYZwYFtLJom4ioIngKBfY4YpRI4aWEKq4vRXSPlGEGptewYaAZ1+eJ/WTMkZlfHtarFxN48iDPXAAjgAG56ACbkAV1AAFj+AZvII358l5cd6dj0lrzpnO7II/cD5/AGmrmDA=</latexit><latexit sha1_base64="xE+HyrM0hByfFs3/ZqepnKJFRUQ=">AAACCnicbVDLSgMxFM3UV62vUZduokVwUUsiim6EohuXFewDOmPJpGkbmswMSUYow6zd+CtuXCji1i9w59+YPhbaeuDC4Zx7ufeeIBZcG4S+ndzC4tLySn61sLa+sbnlbu/UdZQoymo0EpFqBkQzwUNWM9wI1owVIzIQrBEMrkd+44EpzaPwzgxj5kvSC3mXU2Ks1Hb3VRtfotIZ9AyXTEOM7tNjjDKvBFNPSSiztltEZTQGnCd4Sopgimrb/fI6EU0kCw0VROsWRrHxU6IMp4JlBS/RLCZ0QHqsZWlI7F4/Hb+SwUOrdGA3UrZCA8fq74mUSK2HMrCdkpi+nvVG4n9eKzHdCz/lYZwYFtLJom4ioIngKBfY4YpRI4aWEKq4vRXSPlGEGptewYaAZ1+eJ/WTMkZlfHtarFxN48iDPXAAjgAG56ACbkAV1AAFj+AZvII358l5cd6dj0lrzpnO7II/cD5/AGmrmDA=</latexit>

Transições discretas

Page 12: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

QUANTIZAÇÃO A LA BOHR III E SERIE DE BALMER

1

�= R

✓1

22� 1

n2

<latexit sha1_base64="YFTWeR+vLszpyyiXf8Qp44GsgTw=">AAACJHicbVDLSsNAFJ34rPVVdekmWIS6sCRFUBSh4MZlFfuAJpbJZNIOnUzCzI1QQj7Gjb/ixoUPXLjxW5w+KNp6YeDcc+7hzj1ezJkCy/oyFhaXlldWc2v59Y3Nre3Czm5DRYkktE4iHsmWhxXlTNA6MOC0FUuKQ4/Tpte/GurNByoVi8QdDGLqhrgrWMAIBk11ChdOIDFJ7Sx1uHb5OLu8dTgNoDQVKveV7HjaCd05knV7cNQpFK2yNSpzHtgTUESTqnUK744fkSSkAgjHSrVtKwY3xRIY4TTLO4miMSZ93KVtDQUOqXLT0ZGZeagZ3wwiqZ8Ac8T+dqQ4VGoQenoyxNBTs9qQ/E9rJxCcuSkTcQJUkPGiIOEmROYwMdNnkhLgAw0wkUz/1SQ9rOMAnWteh2DPnjwPGpWybZXtm5Ni9XwSRw7towNUQjY6RVV0jWqojgh6RM/oFb0ZT8aL8WF8jkcXjIlnD/0p4/sHfrGlRw==</latexit><latexit sha1_base64="YFTWeR+vLszpyyiXf8Qp44GsgTw=">AAACJHicbVDLSsNAFJ34rPVVdekmWIS6sCRFUBSh4MZlFfuAJpbJZNIOnUzCzI1QQj7Gjb/ixoUPXLjxW5w+KNp6YeDcc+7hzj1ezJkCy/oyFhaXlldWc2v59Y3Nre3Czm5DRYkktE4iHsmWhxXlTNA6MOC0FUuKQ4/Tpte/GurNByoVi8QdDGLqhrgrWMAIBk11ChdOIDFJ7Sx1uHb5OLu8dTgNoDQVKveV7HjaCd05knV7cNQpFK2yNSpzHtgTUESTqnUK744fkSSkAgjHSrVtKwY3xRIY4TTLO4miMSZ93KVtDQUOqXLT0ZGZeagZ3wwiqZ8Ac8T+dqQ4VGoQenoyxNBTs9qQ/E9rJxCcuSkTcQJUkPGiIOEmROYwMdNnkhLgAw0wkUz/1SQ9rOMAnWteh2DPnjwPGpWybZXtm5Ni9XwSRw7towNUQjY6RVV0jWqojgh6RM/oFb0ZT8aL8WF8jkcXjIlnD/0p4/sHfrGlRw==</latexit><latexit sha1_base64="YFTWeR+vLszpyyiXf8Qp44GsgTw=">AAACJHicbVDLSsNAFJ34rPVVdekmWIS6sCRFUBSh4MZlFfuAJpbJZNIOnUzCzI1QQj7Gjb/ixoUPXLjxW5w+KNp6YeDcc+7hzj1ezJkCy/oyFhaXlldWc2v59Y3Nre3Czm5DRYkktE4iHsmWhxXlTNA6MOC0FUuKQ4/Tpte/GurNByoVi8QdDGLqhrgrWMAIBk11ChdOIDFJ7Sx1uHb5OLu8dTgNoDQVKveV7HjaCd05knV7cNQpFK2yNSpzHtgTUESTqnUK744fkSSkAgjHSrVtKwY3xRIY4TTLO4miMSZ93KVtDQUOqXLT0ZGZeagZ3wwiqZ8Ac8T+dqQ4VGoQenoyxNBTs9qQ/E9rJxCcuSkTcQJUkPGiIOEmROYwMdNnkhLgAw0wkUz/1SQ9rOMAnWteh2DPnjwPGpWybZXtm5Ni9XwSRw7towNUQjY6RVV0jWqojgh6RM/oFb0ZT8aL8WF8jkcXjIlnD/0p4/sHfrGlRw==</latexit><latexit sha1_base64="YFTWeR+vLszpyyiXf8Qp44GsgTw=">AAACJHicbVDLSsNAFJ34rPVVdekmWIS6sCRFUBSh4MZlFfuAJpbJZNIOnUzCzI1QQj7Gjb/ixoUPXLjxW5w+KNp6YeDcc+7hzj1ezJkCy/oyFhaXlldWc2v59Y3Nre3Czm5DRYkktE4iHsmWhxXlTNA6MOC0FUuKQ4/Tpte/GurNByoVi8QdDGLqhrgrWMAIBk11ChdOIDFJ7Sx1uHb5OLu8dTgNoDQVKveV7HjaCd05knV7cNQpFK2yNSpzHtgTUESTqnUK744fkSSkAgjHSrVtKwY3xRIY4TTLO4miMSZ93KVtDQUOqXLT0ZGZeagZ3wwiqZ8Ac8T+dqQ4VGoQenoyxNBTs9qQ/E9rJxCcuSkTcQJUkPGiIOEmROYwMdNnkhLgAw0wkUz/1SQ9rOMAnWteh2DPnjwPGpWybZXtm5Ni9XwSRw7towNUQjY6RVV0jWqojgh6RM/oFb0ZT8aL8WF8jkcXjIlnD/0p4/sHfrGlRw==</latexit>

Podemos transformar

(hc)

�= (hc)R

✓1

22� 1

n2

<latexit sha1_base64="acHRnOHO34gtwqasq2i9tjwCw1o=">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</latexit><latexit sha1_base64="acHRnOHO34gtwqasq2i9tjwCw1o=">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</latexit><latexit sha1_base64="acHRnOHO34gtwqasq2i9tjwCw1o=">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</latexit><latexit sha1_base64="acHRnOHO34gtwqasq2i9tjwCw1o=">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</latexit>

| {z }<latexit sha1_base64="hmsPSOEnAtRLejkxlTKThK2sAnU=">AAACCnicbVDLSsNAFJ34rPUVdelmtAiuSiKCLotuXFawD2hDmUxu2qGTSZyHUELXbvwVNy4UcesXuPNvnLZZaOuBezmccy8z94QZZ0p73reztLyyurZe2ihvbm3v7Lp7+02VGkmhQVOeynZIFHAmoKGZ5tDOJJAk5NAKh9cTv/UAUrFU3OlRBkFC+oLFjBJtpZ571DUiAhlKQiHv3hsSzbVxz614VW8KvEj8glRQgXrP/epGKTUJCE05Uarje5kOciI1oxzG5a5RkBE6JH3oWCpIAirIp6eM8YlVIhyn0pbQeKr+3shJotQoCe1kQvRAzXsT8T+vY3R8GeRMZEaDoLOHYsOxTvEkFxwxCVTzkSWESmb/iumA2Fi0Ta9sQ/DnT14kzbOq71X92/NK7aqIo4QO0TE6RT66QDV0g+qogSh6RM/oFb05T86L8+58zEaXnGLnAP2B8/kDqsGbgA==</latexit><latexit sha1_base64="hmsPSOEnAtRLejkxlTKThK2sAnU=">AAACCnicbVDLSsNAFJ34rPUVdelmtAiuSiKCLotuXFawD2hDmUxu2qGTSZyHUELXbvwVNy4UcesXuPNvnLZZaOuBezmccy8z94QZZ0p73reztLyyurZe2ihvbm3v7Lp7+02VGkmhQVOeynZIFHAmoKGZ5tDOJJAk5NAKh9cTv/UAUrFU3OlRBkFC+oLFjBJtpZ571DUiAhlKQiHv3hsSzbVxz614VW8KvEj8glRQgXrP/epGKTUJCE05Uarje5kOciI1oxzG5a5RkBE6JH3oWCpIAirIp6eM8YlVIhyn0pbQeKr+3shJotQoCe1kQvRAzXsT8T+vY3R8GeRMZEaDoLOHYsOxTvEkFxwxCVTzkSWESmb/iumA2Fi0Ta9sQ/DnT14kzbOq71X92/NK7aqIo4QO0TE6RT66QDV0g+qogSh6RM/oFb05T86L8+58zEaXnGLnAP2B8/kDqsGbgA==</latexit><latexit sha1_base64="hmsPSOEnAtRLejkxlTKThK2sAnU=">AAACCnicbVDLSsNAFJ34rPUVdelmtAiuSiKCLotuXFawD2hDmUxu2qGTSZyHUELXbvwVNy4UcesXuPNvnLZZaOuBezmccy8z94QZZ0p73reztLyyurZe2ihvbm3v7Lp7+02VGkmhQVOeynZIFHAmoKGZ5tDOJJAk5NAKh9cTv/UAUrFU3OlRBkFC+oLFjBJtpZ571DUiAhlKQiHv3hsSzbVxz614VW8KvEj8glRQgXrP/epGKTUJCE05Uarje5kOciI1oxzG5a5RkBE6JH3oWCpIAirIp6eM8YlVIhyn0pbQeKr+3shJotQoCe1kQvRAzXsT8T+vY3R8GeRMZEaDoLOHYsOxTvEkFxwxCVTzkSWESmb/iumA2Fi0Ta9sQ/DnT14kzbOq71X92/NK7aqIo4QO0TE6RT66QDV0g+qogSh6RM/oFb05T86L8+58zEaXnGLnAP2B8/kDqsGbgA==</latexit><latexit sha1_base64="hmsPSOEnAtRLejkxlTKThK2sAnU=">AAACCnicbVDLSsNAFJ34rPUVdelmtAiuSiKCLotuXFawD2hDmUxu2qGTSZyHUELXbvwVNy4UcesXuPNvnLZZaOuBezmccy8z94QZZ0p73reztLyyurZe2ihvbm3v7Lp7+02VGkmhQVOeynZIFHAmoKGZ5tDOJJAk5NAKh9cTv/UAUrFU3OlRBkFC+oLFjBJtpZ571DUiAhlKQiHv3hsSzbVxz614VW8KvEj8glRQgXrP/epGKTUJCE05Uarje5kOciI1oxzG5a5RkBE6JH3oWCpIAirIp6eM8YlVIhyn0pbQeKr+3shJotQoCe1kQvRAzXsT8T+vY3R8GeRMZEaDoLOHYsOxTvEkFxwxCVTzkSWESmb/iumA2Fi0Ta9sQ/DnT14kzbOq71X92/NK7aqIo4QO0TE6RT66QDV0g+qogSh6RM/oFb05T86L8+58zEaXnGLnAP2B8/kDqsGbgA==</latexit>

energia de um foton

Diferença da energia de um elétronz }| {

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Page 13: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

QUANTIZAÇÃO A LA BOHR III E TODAS AS SERIES

Page 14: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

MECÂNICA QUÂNTICA

n é chamado número quântico principal(hc)

�= (hc)R

✓1

22� 1

n2

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MECÂNICA QUÂNTICA: OUTROS NÚMEROS QUÂNTICOS

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ml<latexit sha1_base64="qYInBXI/Vsc0mXCcC9MrcdT9dEU=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9WX/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/U8CNzg==</latexit><latexit sha1_base64="qYInBXI/Vsc0mXCcC9MrcdT9dEU=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9WX/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/U8CNzg==</latexit><latexit sha1_base64="qYInBXI/Vsc0mXCcC9MrcdT9dEU=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9WX/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/U8CNzg==</latexit><latexit sha1_base64="qYInBXI/Vsc0mXCcC9MrcdT9dEU=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9WX/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/U8CNzg==</latexit> :número quântico magnetico �l < ml < l

<latexit sha1_base64="ZGlYt8Z+FsWhhr+qjPeWlc+fKLg=">AAAB8XicbVDLSgNBEOyNrxhfUY9eBoPgxbArgh5yCHjxGME8MFnC7GQ2GTKPZWZWCEv+wosHRbz6N978GyfJHjSxoKGo6qa7K0o4M9b3v73C2vrG5lZxu7Szu7d/UD48ahmVakKbRHGlOxE2lDNJm5ZZTjuJplhEnLaj8e3Mbz9RbZiSD3aS0FDgoWQxI9g66fGCoxoSfV7j/XLFr/pzoFUS5KQCORr98ldvoEgqqLSEY2O6gZ/YMMPaMsLptNRLDU0wGeMh7ToqsaAmzOYXT9GZUwYoVtqVtGiu/p7IsDBmIiLXKbAdmWVvJv7ndVMb34QZk0lqqSSLRXHKkVVo9j4aME2J5RNHMNHM3YrICGtMrAup5EIIll9eJa3LauBXg/urSr2ex1GEEziFcwjgGupwBw1oAgEJz/AKb57xXrx372PRWvDymWP4A+/zBwN7j9E=</latexit><latexit sha1_base64="ZGlYt8Z+FsWhhr+qjPeWlc+fKLg=">AAAB8XicbVDLSgNBEOyNrxhfUY9eBoPgxbArgh5yCHjxGME8MFnC7GQ2GTKPZWZWCEv+wosHRbz6N978GyfJHjSxoKGo6qa7K0o4M9b3v73C2vrG5lZxu7Szu7d/UD48ahmVakKbRHGlOxE2lDNJm5ZZTjuJplhEnLaj8e3Mbz9RbZiSD3aS0FDgoWQxI9g66fGCoxoSfV7j/XLFr/pzoFUS5KQCORr98ldvoEgqqLSEY2O6gZ/YMMPaMsLptNRLDU0wGeMh7ToqsaAmzOYXT9GZUwYoVtqVtGiu/p7IsDBmIiLXKbAdmWVvJv7ndVMb34QZk0lqqSSLRXHKkVVo9j4aME2J5RNHMNHM3YrICGtMrAup5EIIll9eJa3LauBXg/urSr2ex1GEEziFcwjgGupwBw1oAgEJz/AKb57xXrx372PRWvDymWP4A+/zBwN7j9E=</latexit><latexit sha1_base64="ZGlYt8Z+FsWhhr+qjPeWlc+fKLg=">AAAB8XicbVDLSgNBEOyNrxhfUY9eBoPgxbArgh5yCHjxGME8MFnC7GQ2GTKPZWZWCEv+wosHRbz6N978GyfJHjSxoKGo6qa7K0o4M9b3v73C2vrG5lZxu7Szu7d/UD48ahmVakKbRHGlOxE2lDNJm5ZZTjuJplhEnLaj8e3Mbz9RbZiSD3aS0FDgoWQxI9g66fGCoxoSfV7j/XLFr/pzoFUS5KQCORr98ldvoEgqqLSEY2O6gZ/YMMPaMsLptNRLDU0wGeMh7ToqsaAmzOYXT9GZUwYoVtqVtGiu/p7IsDBmIiLXKbAdmWVvJv7ndVMb34QZk0lqqSSLRXHKkVVo9j4aME2J5RNHMNHM3YrICGtMrAup5EIIll9eJa3LauBXg/urSr2ex1GEEziFcwjgGupwBw1oAgEJz/AKb57xXrx372PRWvDymWP4A+/zBwN7j9E=</latexit><latexit sha1_base64="ZGlYt8Z+FsWhhr+qjPeWlc+fKLg=">AAAB8XicbVDLSgNBEOyNrxhfUY9eBoPgxbArgh5yCHjxGME8MFnC7GQ2GTKPZWZWCEv+wosHRbz6N978GyfJHjSxoKGo6qa7K0o4M9b3v73C2vrG5lZxu7Szu7d/UD48ahmVakKbRHGlOxE2lDNJm5ZZTjuJplhEnLaj8e3Mbz9RbZiSD3aS0FDgoWQxI9g66fGCoxoSfV7j/XLFr/pzoFUS5KQCORr98ldvoEgqqLSEY2O6gZ/YMMPaMsLptNRLDU0wGeMh7ToqsaAmzOYXT9GZUwYoVtqVtGiu/p7IsDBmIiLXKbAdmWVvJv7ndVMb34QZk0lqqSSLRXHKkVVo9j4aME2J5RNHMNHM3YrICGtMrAup5EIIll9eJa3LauBXg/urSr2ex1GEEziFcwjgGupwBw1oAgEJz/AKb57xXrx372PRWvDymWP4A+/zBwN7j9E=</latexit>

ms<latexit sha1_base64="ZNQJo/PDiatUC8WpzlhtC/ecq4o=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9W3/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/XlyN1Q==</latexit><latexit sha1_base64="ZNQJo/PDiatUC8WpzlhtC/ecq4o=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9W3/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/XlyN1Q==</latexit><latexit sha1_base64="ZNQJo/PDiatUC8WpzlhtC/ecq4o=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9W3/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/XlyN1Q==</latexit><latexit sha1_base64="ZNQJo/PDiatUC8WpzlhtC/ecq4o=">AAAB6nicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DJgYxnRxEByhL3NXrJkd+/YnRPCkZ9gY6GIrb/Izn/jJrlCEx8MPN6bYWZelEph0fe/vdLa+sbmVnm7srO7t39QPTxq2yQzjLdYIhPTiajlUmjeQoGSd1LDqYokf4zGNzP/8YkbKxL9gJOUh4oOtYgFo+ike9W3/WrNr/tzkFUSFKQGBZr96ldvkLBMcY1MUmu7gZ9imFODgk k+rfQyy1PKxnTIu45qqrgN8/mpU3LmlAGJE+NKI5mrvydyqqydqMh1Kooju+zNxP+8bobxdZgLnWbINVssijNJMCGzv8lAGM5QThyhzAh3K2EjaihDl07FhRAsv7xK2hf1wK8Hd5e1RqOIowwncArnEMAVNOAWmtACBkN4hld486T34r17H4vWklfMHMMfeJ8/XlyN1Q==</latexit>

:número quântico de spin ms = ±1

2<latexit sha1_base64="gFsm5INnnIMQyETYfNbxJ6mT81o=">AAAB/HicbVBNS8NAEJ3Ur1q/oj16WSyCp5IUQS9CwYvHCvYDmhA22027dDcJuxshhPpXvHhQxKs/xJv/xm2bg7Y+GHi8N8PMvDDlTGnH+bYqG5tb2zvV3dre/sHhkX180lNJJgntkoQnchBiRTmLaVczzekglRSLkNN+OL2d+/1HKhVL4gedp9QXeByziBGsjRTYdRGoGy8VyIskJoU7K1qzwG44TWcBtE7ckjSgRCewv7xRQjJBY004VmroOqn2Cyw1I5zOal6maIrJFI/p0NAYC6r8YnH8DJ0bZYSiRJqKNVqovycKLJTKRWg6BdYTterNxf+8Yaaja79gcZppGpPloijjSCdongQaMUmJ5rkhmEhmbkVkgk0K2uRVMyG4qy+vk16r6TpN9/6y0W6XcVThFM7gAly4gjbcQQe6QCCHZ3iFN+vJerHerY9la8UqZ+rwB9bnD03tlIc=</latexit><latexit sha1_base64="gFsm5INnnIMQyETYfNbxJ6mT81o=">AAAB/HicbVBNS8NAEJ3Ur1q/oj16WSyCp5IUQS9CwYvHCvYDmhA22027dDcJuxshhPpXvHhQxKs/xJv/xm2bg7Y+GHi8N8PMvDDlTGnH+bYqG5tb2zvV3dre/sHhkX180lNJJgntkoQnchBiRTmLaVczzekglRSLkNN+OL2d+/1HKhVL4gedp9QXeByziBGsjRTYdRGoGy8VyIskJoU7K1qzwG44TWcBtE7ckjSgRCewv7xRQjJBY004VmroOqn2Cyw1I5zOal6maIrJFI/p0NAYC6r8YnH8DJ0bZYSiRJqKNVqovycKLJTKRWg6BdYTterNxf+8Yaaja79gcZppGpPloijjSCdongQaMUmJ5rkhmEhmbkVkgk0K2uRVMyG4qy+vk16r6TpN9/6y0W6XcVThFM7gAly4gjbcQQe6QCCHZ3iFN+vJerHerY9la8UqZ+rwB9bnD03tlIc=</latexit><latexit sha1_base64="gFsm5INnnIMQyETYfNbxJ6mT81o=">AAAB/HicbVBNS8NAEJ3Ur1q/oj16WSyCp5IUQS9CwYvHCvYDmhA22027dDcJuxshhPpXvHhQxKs/xJv/xm2bg7Y+GHi8N8PMvDDlTGnH+bYqG5tb2zvV3dre/sHhkX180lNJJgntkoQnchBiRTmLaVczzekglRSLkNN+OL2d+/1HKhVL4gedp9QXeByziBGsjRTYdRGoGy8VyIskJoU7K1qzwG44TWcBtE7ckjSgRCewv7xRQjJBY004VmroOqn2Cyw1I5zOal6maIrJFI/p0NAYC6r8YnH8DJ0bZYSiRJqKNVqovycKLJTKRWg6BdYTterNxf+8Yaaja79gcZppGpPloijjSCdongQaMUmJ5rkhmEhmbkVkgk0K2uRVMyG4qy+vk16r6TpN9/6y0W6XcVThFM7gAly4gjbcQQe6QCCHZ3iFN+vJerHerY9la8UqZ+rwB9bnD03tlIc=</latexit><latexit sha1_base64="gFsm5INnnIMQyETYfNbxJ6mT81o=">AAAB/HicbVBNS8NAEJ3Ur1q/oj16WSyCp5IUQS9CwYvHCvYDmhA22027dDcJuxshhPpXvHhQxKs/xJv/xm2bg7Y+GHi8N8PMvDDlTGnH+bYqG5tb2zvV3dre/sHhkX180lNJJgntkoQnchBiRTmLaVczzekglRSLkNN+OL2d+/1HKhVL4gedp9QXeByziBGsjRTYdRGoGy8VyIskJoU7K1qzwG44TWcBtE7ckjSgRCewv7xRQjJBY004VmroOqn2Cyw1I5zOal6maIrJFI/p0NAYC6r8YnH8DJ0bZYSiRJqKNVqovycKLJTKRWg6BdYTterNxf+8Yaaja79gcZppGpPloijjSCdongQaMUmJ5rkhmEhmbkVkgk0K2uRVMyG4qy+vk16r6TpN9/6y0W6XcVThFM7gAly4gjbcQQe6QCCHZ3iFN+vJerHerY9la8UqZ+rwB9bnD03tlIc=</latexit>

Page 15: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

MECÂNICA QUÂNTICA

l=0 s

l=1 p

l=2 f

l=3 g

l=4 h

Page 16: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

MECÂNICA QUÂNTICA

Teoria de Bohr falha

Page 17: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

Unidades de eV

As energias envolvidas aqui são números pequenos.

Para � = 1, 2⇥ 10�10 m<latexit sha1_base64="75eCr56YbZz5cVGIpOO+kzDY6Q8=">AAACDnicbVDLSgMxFM3UV62vUZdugqXgopZJEXQjFN24rGAf0BlLJpNpQ5OZIckIZegXuPFX3LhQxK1rd/6NaTsLbT0QOJxzLjf3+AlnSjvOt1VYWV1b3yhulra2d3b37P2DtopTSWiLxDyWXR8ryllEW5ppTruJpFj4nHb80fXU7zxQqVgc3elxQj2BBxELGcHaSH274nITDvAlqtahq5mgCiLnPjtFzgS61cyVAopJ3y47NWcGuExQTsogR7Nvf7lBTFJBI004VqqHnER7GZaaEU4nJTdVNMFkhAe0Z2iEzV4vm50zgRWjBDCMpXmRhjP190SGhVJj4ZukwHqoFr2p+J/XS3V44WUsSlJNIzJfFKYc6hhOu4EBk5RoPjYEE8nMXyEZYomJNg2WTAlo8eRl0q7XkFNDt2flxlVeRxEcgWNwAhA4Bw1wA5qgBQh4BM/gFbxZT9aL9W59zKMFK585BH9gff4A1biaEQ==</latexit><latexit sha1_base64="75eCr56YbZz5cVGIpOO+kzDY6Q8=">AAACDnicbVDLSgMxFM3UV62vUZdugqXgopZJEXQjFN24rGAf0BlLJpNpQ5OZIckIZegXuPFX3LhQxK1rd/6NaTsLbT0QOJxzLjf3+AlnSjvOt1VYWV1b3yhulra2d3b37P2DtopTSWiLxDyWXR8ryllEW5ppTruJpFj4nHb80fXU7zxQqVgc3elxQj2BBxELGcHaSH274nITDvAlqtahq5mgCiLnPjtFzgS61cyVAopJ3y47NWcGuExQTsogR7Nvf7lBTFJBI004VqqHnER7GZaaEU4nJTdVNMFkhAe0Z2iEzV4vm50zgRWjBDCMpXmRhjP190SGhVJj4ZukwHqoFr2p+J/XS3V44WUsSlJNIzJfFKYc6hhOu4EBk5RoPjYEE8nMXyEZYomJNg2WTAlo8eRl0q7XkFNDt2flxlVeRxEcgWNwAhA4Bw1wA5qgBQh4BM/gFbxZT9aL9W59zKMFK585BH9gff4A1biaEQ==</latexit><latexit sha1_base64="75eCr56YbZz5cVGIpOO+kzDY6Q8=">AAACDnicbVDLSgMxFM3UV62vUZdugqXgopZJEXQjFN24rGAf0BlLJpNpQ5OZIckIZegXuPFX3LhQxK1rd/6NaTsLbT0QOJxzLjf3+AlnSjvOt1VYWV1b3yhulra2d3b37P2DtopTSWiLxDyWXR8ryllEW5ppTruJpFj4nHb80fXU7zxQqVgc3elxQj2BBxELGcHaSH274nITDvAlqtahq5mgCiLnPjtFzgS61cyVAopJ3y47NWcGuExQTsogR7Nvf7lBTFJBI004VqqHnER7GZaaEU4nJTdVNMFkhAe0Z2iEzV4vm50zgRWjBDCMpXmRhjP190SGhVJj4ZukwHqoFr2p+J/XS3V44WUsSlJNIzJfFKYc6hhOu4EBk5RoPjYEE8nMXyEZYomJNg2WTAlo8eRl0q7XkFNDt2flxlVeRxEcgWNwAhA4Bw1wA5qgBQh4BM/gFbxZT9aL9W59zKMFK585BH9gff4A1biaEQ==</latexit><latexit sha1_base64="75eCr56YbZz5cVGIpOO+kzDY6Q8=">AAACDnicbVDLSgMxFM3UV62vUZdugqXgopZJEXQjFN24rGAf0BlLJpNpQ5OZIckIZegXuPFX3LhQxK1rd/6NaTsLbT0QOJxzLjf3+AlnSjvOt1VYWV1b3yhulra2d3b37P2DtopTSWiLxDyWXR8ryllEW5ppTruJpFj4nHb80fXU7zxQqVgc3elxQj2BBxELGcHaSH274nITDvAlqtahq5mgCiLnPjtFzgS61cyVAopJ3y47NWcGuExQTsogR7Nvf7lBTFJBI004VqqHnER7GZaaEU4nJTdVNMFkhAe0Z2iEzV4vm50zgRWjBDCMpXmRhjP190SGhVJj4ZukwHqoFr2p+J/XS3V44WUsSlJNIzJfFKYc6hhOu4EBk5RoPjYEE8nMXyEZYomJNg2WTAlo8eRl0q7XkFNDt2flxlVeRxEcgWNwAhA4Bw1wA5qgBQh4BM/gFbxZT9aL9W59zKMFK585BH9gff4A1biaEQ==</latexit>

qual é a energia?

E =hc

�=

6, 63⇥ 10�34 J.s (3⇥ 108 m/s)

1, 2⇥ 10�10 m= 17⇥ 10�16 J

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Transformando em unidades mais convenientes:

E =(17⇥ 10�16)(1, 6⇥ 10�19 J)

1, 6⇥ 10�19=

(17⇥ 10�16)1 eV

1, 6⇥ 10�19= 10⇥ 103eV

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Page 18: FISICA PARA BIOLOGIA F107 A - Um Blog do Instituto de

TRANSIÇÕES PARA OUTROS ELEMENTOS

1

�= R(Z)2

✓1

(m)2� 1

n2

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onde m e n são os números principais

Seja a transição do Hidrogênio entre n=1 e n=4. Qual � ?<latexit sha1_base64="CFnnwTTrCTJjqIXPX3lbuLApDfA=">AAAB/HicbVDLSsNAFL2pr1pf0S7dDBbBhZREBN1ZcOOygn1AE8pkMmmHziRhZiKEUH/FjQtF3Poh7vwbp20W2npg4HDOudw7J0g5U9pxvq3K2vrG5lZ1u7azu7d/YB8edVWSSUI7JOGJ7AdYUc5i2tFMc9pPJcUi4LQXTG5nfu+RSsWS+EHnKfUFHsUsYgRrIw3tusdNOMTIO0eFJwVCN9Oh3XCazhxolbglaUCJ9tD+8sKEZILGmnCs1MB1Uu0XWGpGOJ3WvEzRFJMJHtGBoTEWVPnF/PgpOjVKiKJEmhdrNFd/TxRYKJWLwCQF1mO17M3E/7xBpqNrv2Bxmmkak8WiKONIJ2jWBAqZpETz3BBMJDO3IjLGEhNt+qqZEtzlL6+S7kXTdZru/WWj1SrrqMIxnMAZuHAFLbiDNnSAQA7P8Apv1pP1Yr1bH4toxSpn6vAH1ucP6COTng==</latexit><latexit sha1_base64="CFnnwTTrCTJjqIXPX3lbuLApDfA=">AAAB/HicbVDLSsNAFL2pr1pf0S7dDBbBhZREBN1ZcOOygn1AE8pkMmmHziRhZiKEUH/FjQtF3Poh7vwbp20W2npg4HDOudw7J0g5U9pxvq3K2vrG5lZ1u7azu7d/YB8edVWSSUI7JOGJ7AdYUc5i2tFMc9pPJcUi4LQXTG5nfu+RSsWS+EHnKfUFHsUsYgRrIw3tusdNOMTIO0eFJwVCN9Oh3XCazhxolbglaUCJ9tD+8sKEZILGmnCs1MB1Uu0XWGpGOJ3WvEzRFJMJHtGBoTEWVPnF/PgpOjVKiKJEmhdrNFd/TxRYKJWLwCQF1mO17M3E/7xBpqNrv2Bxmmkak8WiKONIJ2jWBAqZpETz3BBMJDO3IjLGEhNt+qqZEtzlL6+S7kXTdZru/WWj1SrrqMIxnMAZuHAFLbiDNnSAQA7P8Apv1pP1Yr1bH4toxSpn6vAH1ucP6COTng==</latexit><latexit sha1_base64="CFnnwTTrCTJjqIXPX3lbuLApDfA=">AAAB/HicbVDLSsNAFL2pr1pf0S7dDBbBhZREBN1ZcOOygn1AE8pkMmmHziRhZiKEUH/FjQtF3Poh7vwbp20W2npg4HDOudw7J0g5U9pxvq3K2vrG5lZ1u7azu7d/YB8edVWSSUI7JOGJ7AdYUc5i2tFMc9pPJcUi4LQXTG5nfu+RSsWS+EHnKfUFHsUsYgRrIw3tusdNOMTIO0eFJwVCN9Oh3XCazhxolbglaUCJ9tD+8sKEZILGmnCs1MB1Uu0XWGpGOJ3WvEzRFJMJHtGBoTEWVPnF/PgpOjVKiKJEmhdrNFd/TxRYKJWLwCQF1mO17M3E/7xBpqNrv2Bxmmkak8WiKONIJ2jWBAqZpETz3BBMJDO3IjLGEhNt+qqZEtzlL6+S7kXTdZru/WWj1SrrqMIxnMAZuHAFLbiDNnSAQA7P8Apv1pP1Yr1bH4toxSpn6vAH1ucP6COTng==</latexit><latexit sha1_base64="CFnnwTTrCTJjqIXPX3lbuLApDfA=">AAAB/HicbVDLSsNAFL2pr1pf0S7dDBbBhZREBN1ZcOOygn1AE8pkMmmHziRhZiKEUH/FjQtF3Poh7vwbp20W2npg4HDOudw7J0g5U9pxvq3K2vrG5lZ1u7azu7d/YB8edVWSSUI7JOGJ7AdYUc5i2tFMc9pPJcUi4LQXTG5nfu+RSsWS+EHnKfUFHsUsYgRrIw3tusdNOMTIO0eFJwVCN9Oh3XCazhxolbglaUCJ9tD+8sKEZILGmnCs1MB1Uu0XWGpGOJ3WvEzRFJMJHtGBoTEWVPnF/PgpOjVKiKJEmhdrNFd/TxRYKJWLwCQF1mO17M3E/7xBpqNrv2Bxmmkak8WiKONIJ2jWBAqZpETz3BBMJDO3IjLGEhNt+qqZEtzlL6+S7kXTdZru/WWj1SrrqMIxnMAZuHAFLbiDNnSAQA7P8Apv1pP1Yr1bH4toxSpn6vAH1ucP6COTng==</latexit>

1

�= 8, 2⇥ 106 m�1 ! � = 1, 2⇥ 10�8 m = 12nm

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1

�= 1, 4⇥ 1010 m�1 ! � = 7, 2⇥ 10�10 m = 0, 072 nm

<latexit sha1_base64="K5OOX3mVBL3mS9U6Lqc8Jp5NPIw=">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</latexit><latexit sha1_base64="K5OOX3mVBL3mS9U6Lqc8Jp5NPIw=">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</latexit><latexit sha1_base64="K5OOX3mVBL3mS9U6Lqc8Jp5NPIw=">AAACVnicbVHLSgMxFM2Mr1pfoy7dBIvgopakFOqmUHDjsoJVoVNLJs1oMMkMSUYoYX5SN/opbsS0juDrQuBwHuTmJMkFNxah1yBcWl5ZXaut1zc2t7Z3ot29K5MVmrIhzUSmbxJimOCKDS23gt3kmhGZCHadPJzN9etHpg3P1KWd5WwsyZ3iKafEemoSyTjVhDpculj41JSUPdzswNhyyQzE6NZhVMZN6GItoSxv3QkuvZrByt7rNtvfzCcLd2XuoSbqtuFXWslyEjVQCy0G/gW4Ag1QzWASPcXTjBaSKUsFMWaEUW7HjmjLqWBlPS4Mywl9IHds5KEifpGxW9RSwiPPTGGaaX+UhQv2e8IRacxMJt4pib03v7U5+Z82Kmx6OnZc5YVlin5elBYC+lrmHcMp14xaMfOAUM39rpDeE9+z9T9R9yXg30/+C67aLYxa+KLT6PerOmrgAByCY4BBF/TBORiAIaDgGbwFYbAUvATv4Uq49mkNgyqzD35MGH0AMBav5w==</latexit><latexit sha1_base64="K5OOX3mVBL3mS9U6Lqc8Jp5NPIw=">AAACVnicbVHLSgMxFM2Mr1pfoy7dBIvgopakFOqmUHDjsoJVoVNLJs1oMMkMSUYoYX5SN/opbsS0juDrQuBwHuTmJMkFNxah1yBcWl5ZXaut1zc2t7Z3ot29K5MVmrIhzUSmbxJimOCKDS23gt3kmhGZCHadPJzN9etHpg3P1KWd5WwsyZ3iKafEemoSyTjVhDpculj41JSUPdzswNhyyQzE6NZhVMZN6GItoSxv3QkuvZrByt7rNtvfzCcLd2XuoSbqtuFXWslyEjVQCy0G/gW4Ag1QzWASPcXTjBaSKUsFMWaEUW7HjmjLqWBlPS4Mywl9IHds5KEifpGxW9RSwiPPTGGaaX+UhQv2e8IRacxMJt4pib03v7U5+Z82Kmx6OnZc5YVlin5elBYC+lrmHcMp14xaMfOAUM39rpDeE9+z9T9R9yXg30/+C67aLYxa+KLT6PerOmrgAByCY4BBF/TBORiAIaDgGbwFYbAUvATv4Uq49mkNgyqzD35MGH0AMBav5w==</latexit>

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TRANSIÇÕES PARA OUTROS ELEMENTOS

Dado o electron mais externo

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da transição deste elétron para o estado fundamental.

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TABELA PERIODICA

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TABELA PERIODICA

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RESUMO:

Ondas: interferência e difração

Fenda simples, fenda dupla : achar máximos e mínimos

Comprimento de onda de Broglie: partículas

Interferencia de electrons e difração: comprimento de onda X tamanho da fenda

Modelo atômico: espectros discretos de átomos isolados/ absorção

Modelo de Bohr: orbitas discretas -> transições discretas (Serie de Balmer)

Átomos mais pesados, “modelo de Bohr”