physics quiz
The Cosmic Background Radiation Outer space is filled with a sea of photons, created in the early moments of the universe. The frequency distribution of this “cosmic background radiation” matches that of a blackbody at a temperature near 2.7K. (a) What is the peak frequency of this radiation? (b) What is the wavelength that corresponds to the peak frequency?
Given,
Temperature (T) = 2.7K
- Peak frequency is represented as
fpeak = T (5.88 * 1010 s-1 * K-1)
Substitute 2.7K for T
fpeak = (2.7K) (5.88 * 1010 s-1 * K-1)
fpeak = 1.5876 x 1011 Hz
The peak frequency of this radiation 1.5876 x 1011 Hz.
- Wavelength of the peak frequency
c = f
Rearrange
Substitute in the proper values into the equation. The numerator represents the speed of light in a vacuum, which is The denominator represents the peak frequency, which is
Dividing m/s by Hz will give us a final unit of meters.
The wavelength that corresponds to the peak frequency 1
34. Predict/Calculate Platinum has a work function of 6.35 eV, and iron has a work of 4.50 eV. Light of frequency 1.88 x 10-19 J ejects electrons from both of these surfaces. (a) From which surface will the ejected electrons have a greater maximum kinetic energy? Explain. (b) Calculate the maximum kinetic energy of ejected electrons for each surface.
42. A hydrogen atom, initially at rest, emits an ultraviolet photon with a wavelength of What is the recoil speed of the atom after emitting the photon?
Momentum of photon
p =
Momentum of hydrogen atom is represented as
p =
Pphoto = PH
=
v)2 = (
2
(v)2 =
+
(v)2 =
v2 [ +
] = 1
v = [ +
]-1/2
v = c [1 + ]-1/2
Now, substitute in the proper values
Wavelength is 122 nm = 122 x 109 m
Planck’s constant = 6.63 x 10-34 J*s
Mass of hydrogen atom = 1.674 x 10-27 kg
Speed of light (c) =
v = 3 x 108 m/s [1+]-1/2
v = 3.25 m/s
Thus, the recoil speed of the atom after emitting the photon is 3.25 m/s.
52. In the Compton effect, an X-ray photon scatters from a free electron. Find the change in the photon’s wavelength if it scatters at an angle of (a) , (b)
90.0º, and (c)
relative to the incident direction.
67. Predict/Calculate An electron and a proton have the same de Broglie wavelength. (a) Which has the greater kinetic energy? Explain. (b) Calculate the ratio (e/
p).
76. Quantum Well A quantum well is a region of semiconductor or metal film that confines particles to a small region, resulting in quantized energies that are useful for the operation of a variety of electronic devices. If an electron in a quantum well is confined to an area that is 510 nm wide, what is the uncertainty in the electron’s velocity along the same direction?
