Lecture 36

Summary

Photoelectric effect
de Broglie hypothesis
Bohr model

Quiz bonus Chs. 30-31

Bohr model review

Example #1

Example #2

Electrons are waves

IBM researchers used a scanning tunneling microscope to arrange Xe atoms on a chilled Ni surface. (Discussion and video) The trapped electrons demonstrate their wave nature via Freidel oscillations. More info from UW Madison Materials Research.

The QM atom [skipped]

Schrödinger equation
energy levels
four quantum numbers
The Pauli exclusion principle
electron wave functions applet
H orbitals

Example #3

The periodic table

Example #4

filling electron shells to explain the periodic table

X-ray emission (Section 31-7)

X-ray tubes
electron shielding
approximate energy levels

Example #5

Lasers

spontaneous emission
stimulated emission applet
laser operation

Example #6

Lecture learning outcomes
A student who masters the topics in this lecture will be able to:

describe how de Broglie waves explained why electrons in allowed orbits do not radiate
describe the basic features of the quantum mechanical model of the atom
explain how an X-ray tube works
calculate the wavelength of K_α X-rays for an element of atomic number Z
describe the operating principles of a laser, and calculate the energy delivered by laser beam during a time interval Δt when given the beam intensity I and cross-sectional area A

Practice:
Try these additional examples

Example #7

Example #8

Prepare:
Read textbook sections 32-1 and 32-2 before the next lecture

Walker5e CnEx 30-8

A beam of light with a frequency greater than the cutoff frequency shines on the emitter. If the frequency of the light is increased (the color is made bluer) while the intensity (energy per time) is held constant, the number of electrons ejected per second from the emitter will _____.
photoelectric effect apparatus

A. increase
B. decrease
C. stay the same
Answer

klm
According to the Bohr model of the hydrogen atom, when the electron jumps from the n = 2 orbit to the n = 3 orbit its kinetic energy _____.
A. increases
B. decreases
C. stays the same
Answer

Walker5e 31.29
An electron in the n = 5 level of hydrogen remains for 51 ns before jumping down to a lower level. How many orbits did it complete while it was in the n = 5 level?
A. 1.90×10⁻¹⁴ orbits
B. 5 orbits
C. 51 orbits
D. 2.68×10⁶ orbits
Answer

klm
How many different states are possible for an electron whose principal quantum number is n = 4?
A. 8 B. 18 C. 32 D. 50
Answer

sj6 42.38
What is the probable electronic configuration of a neutral atom of element 110?
A. [Rn] 5f¹⁴ 6d² 6f⁶
B. [Rn] 5f¹⁴ 6d⁰ 6f⁸
C. [Rn] 5f¹⁴ 6d⁸ 7s²
D. [Rn] 5f¹⁶ 6d⁶ 7s²
Answer

Walker5 31.61
Using the Bohr model, estimate the energy of a K_α X-ray emitted by lead (Z = 82).
A. 14 keV
B. 67 keV
C. 82 keV
D. 207 keV
Answer

Walker5e 31.84
Suppose a laser emits 1.49×10¹⁹ photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts?
A. 1.49 W
B. 5.76 W
C. 5.91 W
D. 6.07 W
Answer

Walker5e 31.64a
Consider an X-ray tube that uses platinum (Z = 78) as its target. Use the Bohr model to estimate the minimum kinetic energy electrons must have in order for K_α X-rays to just appear in the X-ray spectrum of the tube.
A. 80.6 keV
B. 60.5 keV
C. 20.5 keV
D. 13.6 eV
Answer

Walker5e 31.87
How would the number of photons emitted per second by a yellow laser compare to the number emitted per second by a red laser that has the same power output?
A. The yellow Kr laser emits more photons per second.
B. The yellow Kr laser emits fewer photons per second.
C. The yellow Kr laser emits the same number of photons per second.
Answer

photoelectric effect apparatus

B. decrease
Increasing the frequency of the light means that each photon carries more energy. In order for the intensity to remain constant, there must be fewer photons per second in the beam of light. Because fewer photons hit the surface per second, fewer electrons are ejected per second (but the average kinetic energy of these photoelectrons will be greater because each photon delivers more energy).

B. decreases
According to the Bohr model the speed of the orbiting electron is inversely proportional to the quantum number n, so if the electron jumps to an orbit with a higher n it will slow down and its kinetic energy will decrease.

D. 2.68×10⁶ orbits

solution equation

C. 32

C. [Rn] 5f¹⁴ 6d⁸ 7s²
Use the diagrams above to determine that the 7s subshell will fill up before the 5f or 6d subshells. Along the block of elements from 103 to 112 the 6d subshell is being filled. There is in reality an anomaly here and the actual observed configuration is 5f¹⁴ 6d⁹ 7s¹.
fill shells element 110 to find configuration

fill shells element 110 to find configuration

B. 67 keV

C. 5.91 W

Each photon contributes to the total power delivered by the laser beam.

solution equation

A. 80.6 keV

Follow the calculation in Quick Example 31-12.

solution equation

B. The yellow Kr laser emits fewer photons per second.

The yellow photons each have more energy than the red photons, hence fewer yellow photons are required to produce the same power output as the red laser. We conclude that the yellow laser emits fewer photons per second.

periodic table