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Chapter 42

Atomic Physics

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Outline

Atomic spectra of gases Early models of the atom Bohr’s model of the hydrogen

atom

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Atomic spectra of gases

(a) Emission line spectra for H, Hg, and Ne.

(b) Absorption spectrum for H.

Orion Nebula

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“Neon” signs: an application

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Balmer series of hydrogen Johann Jocob Balmer (1825-

1898) The empirical equation by

Johannes Rydberg (1854-1919):

RH: Rydberg constant = 1.0973732 x 107 m-1.

The series limit The measured spectral lines

agree with the empirical equation to within 0.1%.

,...5,4,3 1

2

1122

n

nRH

The Balmer series of spectral lines for atomic hydrogen.

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Early models of the atom Model of the atom in

the days of Newton: Tiny, hard, and indestructible sphere.

J.J. Thomson’s model of the atom: Negatively charged electrons in a volume of continuous positive charge.

Rutherford’s planetary model of the atom.

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Difficulties with Rutherford’s planetary model

Cannot explain the phenomenon that an atom emits (and absorbs) certain characteristic frequencies of electromagnetic radiation and no others.

Predication of the ultimate collapse of the atom as the electron plunges into the nucleus.

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Bohr’s model of the hydrogen atom

Basic ideas of the Bohr theory of the hydrogen atom:

The electron moves in circular orbits around the proton under the electric force of attraction.

Only certain electron orbits are stable. When in one of these stationary states, the electron does not emit energy in the form of radiation.

Radiation is emitted by the atom when the electron makes a transition from a more energetic initial orbit to a lower-energy orbit. The frequency of the emitted radiation is found from Ei –Ef = hf. Energy of an incident photon can be absorbed by the atom only if the photon has an energy that exactly matches the difference in energy between an allowed state of the atom and its existing state upon incidence of the photon.

The size of an allowed electron orbit is determined by a condition imposed on the electron’s orbital angular momentum: quantization of the orbital angular momentum mevr=nħ, n = 1,2,3…

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Bohr’s theory of hydrogen atom (cont.)

Allowed energy levels (see detailed derivation):

a0 = Bohr radius = ħ2/mekee2 = 0.0529 nm rn =n2a0 = n2(0.0529 nm) Ionization energy: the minimum energy required

to ionize the atom in its ground state (to completely remove an electron from the proton’s influence) = 13.6 eV for hydrogen.

Emission frequency and wavelength:

,...3,2,1 606.131

2 220

2

neV

nna

ekE en

220

2

220

2

11

2

1

11

2

if

e

if

efi

nnhca

ek

c

f

nnha

ek

h

EEf

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Energy-level diagram for the hydrogen atom

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Quick quiz #1 A hydrogen atom is in its ground

state. Incident on the atom are many photons each having an energy of 10.5 eV. The result is that (a) the atom is excited to a higher

allowed state (b) the atom is ionized (c) the photons pass by the atom

without interaction

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Quick Quiz #2 A hydrogen atom makes a transition from

the n = 3 level to the n = 2 level. It then makes a transition from the n = 2 level to the n = 1 level. Which transition results in emission of the longest-wavelength photon? (a) the first transition (b) the second transition (c) neither, because the wavelengths are the

same for both transitions.

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Homework

Chapter 42, P. 1392, Problems: #5, 6, 8, 12.