Physics 1310
Name:_______________________
Quiz 8c (10 points)
1. An astronomer on Earth observes Galaxy A moving to the left at 0.81c and Galaxy B moving to the
right at 0.83c. A resident of Galaxy B observes a supernova explosion in Galaxy B that lasts 2 months.
Galaxy A
Earth
Galaxy B
From the point of view of an observer in Galaxy A, how long does this supernova explosion last?
VB from A = (VB from Earth + VEarth from A ) / (1 + VB from Earth * VEarth from A / c2 )
= (0.81 c + 0.83 c )/ (1 + 0.81*0.83) = 0.98 c
t = 2 months / sqrt(1-0.982) = 10 months
2. An electron is moving at 70.3% the speed of light. Calculate its relativistic kinetic energy.
KE = E – rest energy = 511 KeV /sqrt(1-0.7032) - 511 KeV
KE = 1011 KeV - 511 KeV = 500 KeV
3. The wavelength corresponding to the peak of a star’s spectrum equals 724.5 nm. What is the
temperature of this star’s surface?
T = 2898 m – K / 724.5 nm = 4000 K
4. A hydrogen atom is initially in its ground state (n = 1). What is the wavelength of the photon that
must be absorbed to move this atom to its first excited state (n = 2)? Is this photon in the visible, UV,
IR, or radio region of the spectrum?
E1 = -13.6 eV
E2 = -13.6 eV / 4 = -3.4 eV
E = 10.2 eV
Ephoton = 10.2 eV
= 1240 eV nm / 10.2 eV = 122 nm, UV
5. An atom is initially in its ground state. It absorbs a photon with wavelength equal to 827 nm and
moves to a metastable excited state. The atom then absorbs a second photon with wavelength equal to
496 nm to move to a higher energy excited state. The atom then emits a photon and falls to the ground
state. What is the wavelength of the emitted photon? Is this photon in the visible, UV, IR, or radio
region of the spectrum?
E first absorbed photon= 1240 nm-eV / 827 nm = 1.50 eV
E second absorbed photon= 1240 nm-eV / 496 nm =2.50 eV
E emitted photon= 2.50 eV + 1.50 eV = 4.00 eV
 emitted photon= 1240 eV nm / 4.00 eV = 310 nm, UV