Problems and Questions

1. What is the size of a bacteria, a large molecule, atom, nucleus, electron and quark?

2. Describe electromagnetic spectrum.

3. Calculate the energy in electron volts of a photon having a wavelength in (a) the

microwave range, 5.00 cm; (b) the visible light range, 500 nm; and (c) the x-ray range,

5.00 nm.

4. Explain Planck’s radical assumption on the light.

5. Are blackbodies black?

6. All objects radiate energy. Why, then, are we not able see all objects in a dark room?

7. Radiation has been detected from space that is characteristic of an ideal radiator at

T=2.728 K (Relic from “Big-Bang”). For this temperature at what wavelength does

the Plank distribution peak? In what part of the electromagnetic spectrum is this

wavelength? Answer: 1.06 μm, microwave

8. A clean nickel surface is exposed to light of wavelength of 235nm. What is the

maximum speed of the photoelectrons emitted from this surface. The work function

for nickel is =5.1 eV. Answer: 2.5x105 m/s

9. The threshold of dark-adapted (scotopic) vision is 4.0x10-11

W/m2 at acentral

wavelength of 500 nm. If light with this intensity and wavelength enters the eye when

the pupil is open to its maximum diameter of 8.5 mm, how many photons per second

enter the eye? Answer: 5.7x103 Photons

10. Calculate the minimum wavelength x-ray that can be produced when a target is struck

by an electron that has been accelerated through a potential difference of (a) 15.0 kV,

(b) 100 kV.

11. Consider Compton scattering with visible light. A photon with wavelength 500 nm

scatters backward ( =180 degrees) from a free electron initially at rest. What is the

fractional shift in wavelength, / for the photon? Answer: 9.7x10-6

12. a) Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the

n=1,2, and 3 levels. b) Calculate the orbital period in each of these levels. c) The

average lifetime of the first excited level of the hydrogen atom is 1.0 x10-8

sec. In the

Bohr model, how many orbits does an electron in the n=2 level complete before

returning to the ground level? Answer: a) v1=2.19x106 m/s, v2=1.09 x10

6 m/s,

v3=7.29x106 m/s b) T1=1.52x10

-16 s, T2=1.22 x10

-15 s, T3=4.10 x10

-15 s c) 8.22x10

6

13. Calculate the de Broglie wavelength of a 5.00 g bullet that is moving at 340 m/s. Will

the bullet exhibit wavelike properties, if yes why, if no why not? Answer: 3.9x10^-34

m, no

14. Which of these continually emits electromagnetic radiation?

a. A flashlight bulb.

b. A hot steam radiator.

c. A tray of ice cubes.

d. None do.

e. All do.

15. It's commonly known that a white-painted house is a good idea in hot summer

weather, because more sunlight is reflected from the exterior, making for a cooler

interior. But what of winter? Is a white-painted house a good or poor idea in cold

winter weather? Defend your answer.

16. In which pot (cup), black or white the water will cool down faster?

17. Which is hotter, a blue flame or an orange one?

18. Surface temperature of sun is 5800 K. Using Wien displacement law calculate

maximum wavelength of the radiated light?

19. Why isn’t the sun blue?

20. Consider a Hydrogen atom in the second excited state (n=3). Use the Bohr model to

answer the following:

a. The maximum number of photons that can be emitted by this atom is two.

Explain.

b. Find the energy (in eV), wavelength (in nm), and momentum (in eV/c) of each

of the photons in (a).

Suppose instead that the excited atom makes one transition to the ground state.

c. Find the energy (in eV), wavelength (in nm), and momentum (in eV/c) of the

single emitted photon.

d. Using conservation of momentum, find the recoil speed of the atom. (A H

atom has a rest mass of 1.007825 u. You can use the nonrelativistic expression

p=Mov since its kinetic energy is much less than its rest energy.)

e. Find the kinetic energy of the recoiling atom in eV. (You can use the

nonrelativistic expression K= p2/2Mo = (1/2)Mov

2.)

f. Compare this recoil energy of the atom to the photon energy found in (c). Are

we justified in neglecting the recoil energy of the atom in calculating the

energies and wavelengths of emitted photons?

21. An electron and a photon each have a wavelength of 5 Å. Find the following

quantitites for each (De Broglie Postulates):

a. momentum, in units of eV/c

b. energy (not including rest energy), in units of eV

c. speed, expressed as a number times c

22. Show that electron does not exist in the nucleus. (use uncertainty principle)

23. Calculate the de Broglie wavelength for an electron that has kinetic energy (a) 50.0 eV

and (b) 50.0 keV (ignore relativistic effects).

24. A 50.0-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.10%,

what is the minimum uncertainty in its position?

25. Does the light emitted by a hydrogen lamp constitute a continuous spectrum or only a

few colors? Defend your answer.

26. If matter has a wave nature, why is this not observable in our daily experience?