Dr. Jie Zou PHY 1371 1

Chapter 42

Atomic Physics

Dr. Jie Zou PHY 1371 2

Outline

Atomic spectra of gases (section 40.4)Early models of the atom (section 42.1)Bohr’s model of the hydrogen atom (section 40.5)

Dr. Jie Zou PHY 1371 3

Atomic spectra of gases

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

(b) Absorption spectrum for H.Orion Nebula

Dr. Jie Zou PHY 1371 4

“Neon” signs: an application

Dr. Jie Zou PHY 1371 5

Balmer series of hydrogenJohann Jocob Balmer (1825-1898)The empirical equation by Johannes Rydberg (1854-1919):

RH: Rydberg constant = 1.0973732 x 107 m-1.The series limitThe measured spectral lines agree with the empirical equation to within 0.1%.

,...5,4,3 1211

22 =⎟⎠⎞

⎜⎝⎛ −= n

nRHλ

The Balmer series of spectral lines for atomic hydrogen.

Dr. Jie Zou PHY 1371 6

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.

Dr. Jie Zou PHY 1371 7

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.

Dr. Jie Zou PHY 1371 8

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…

Dr. Jie Zou PHY 1371 9

Bohr’s theory of hydrogen atom (cont.)

Allowed energy levels (see detailed derivation):

a0 = Bohr radius = ħ2/mekee2 = 0.0529 nmrn =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:

,...3,2,1 606.1312 22

0

2

=−=⎟⎠⎞

⎜⎝⎛−= neV

nnaekE e

n

⎟⎟⎠

⎞⎜⎜⎝

⎛−==

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

−=

220

2

220

2

112

1

112

if

e

if

efi

nnhcaek

cf

nnhaek

hEE

f

λ

Dr. Jie Zou PHY 1371 10

Energy-level diagram for the hydrogen atom

Dr. Jie Zou PHY 1371 11

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

Dr. Jie Zou PHY 1371 12

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.

Dr. Jie Zou PHY 1371 13

Homework

Chapter 40, P. 1317, Problems: #40, 42, 44, 47.