Conceptual Questions:

1. Describe the relationship between the uncertainty principle and the deBroglie wavelength of a particle.

2. Describe how quantum mechanics explains the "photoelectric effect."

3. According to the de Broglie hypothesis, which of the following statements is applicable to the wavelength of a moving particle?

a. directly proportional to its energy
b. directly proportional to its momentum
c. inversely proportional to its energy
d. inversely proportional to its momentum

4. As the temperature of a radiation emitting blackbody becomes higher, what happens to the peak wavelength of the radiation?

a. increases
b. decreases
c. remains constant
d. is directly proportional to temperature

5. According to Einstein, increasing the brightness of a beam of light without changing its color will increase:

a. the number of photons.
b. the energy of each photon.
c. the speed of the photons.
d. the frequency of the photons.

Numerical Problems: help is at the end of the page.

1. Blue light will not eject electrons from a certain metal. Which one of the following may possibly eject electrons from that metal?

a. infra-red
b. ultra-violet
c. red
d. green

2. Photons with wavelength 6.5 x10^-7 m have energy of:

ans: 3.1 x10^-19 J

3. If the measured momentum of an electron is 3.20 x10^-27 kg-m/s with an uncertainty of 1.6 x10^-29 kg-m/s, what is the minimum uncertainty in the determination of its position?

ans: 3.3 x10-6 m

4. What in the de Broglie wavelength for a proton (m = 1.67 x10^-27 kg) moving at a speed of 5.0 x10⁵ m/s?

ans: 0.79 x10^-12 m

5. A sodium vapor lamp has a power output of 300 W. If 590 nm is the average wavelength of the source, about how many photons are emitted per second?

ans: 10²¹

6. The "seeing" ability or resolution of radiation is determined by its wavelength. If the size of an atom is approximately 10^-10 m, how fast must an electron travel to have a wavelength smaller than that of an atom?

ans: 7.28 x10⁶ m/s

Help

1. Does the wavelength have to be shorter or longer?
2. E = h*f = h*c/l
3. Dx = h/4p*Dp
4. l = h/p =h/m*v
5. See Q2
6. See Q4