(III) A certain atom emits light of frequency f 0 when at rest. A monatomic gas composed of these atoms is at temperature T. Some of the gas atoms move toward and others away from an observer due to their random thermal motion. Using the rms speed of thermal motion, show that the fractional difference between the Doppler-shifted frequencies for atoms moving directly toward the observer and directly away from the observer is Δ f / f 0 ≈ 2 3 k T / m c 2 ; assume m c 2 ≫ 3 k T . Evaluate Δ f / f 0 for a gas of hydrogen atoms at 550 K. [This “Doppler-broadening” effect is commonly used to measure gas temperature, such as in astronomy.]
(III) A certain atom emits light of frequency f 0 when at rest. A monatomic gas composed of these atoms is at temperature T. Some of the gas atoms move toward and others away from an observer due to their random thermal motion. Using the rms speed of thermal motion, show that the fractional difference between the Doppler-shifted frequencies for atoms moving directly toward the observer and directly away from the observer is Δ f / f 0 ≈ 2 3 k T / m c 2 ; assume m c 2 ≫ 3 k T . Evaluate Δ f / f 0 for a gas of hydrogen atoms at 550 K. [This “Doppler-broadening” effect is commonly used to measure gas temperature, such as in astronomy.]
(III) A certain atom emits light of frequency f0 when at rest. A monatomic gas composed of these atoms is at temperature T. Some of the gas atoms move toward and others away from an observer due to their random thermal motion. Using the rms speed of thermal motion, show that the fractional difference between the Doppler-shifted frequencies for atoms moving directly toward the observer and directly away from the observer is
Δ
f
/
f
0
≈
2
3
k
T
/
m
c
2
; assume
m
c
2
≫
3
k
T
. Evaluate
Δ
f
/
f
0
for a gas of hydrogen atoms at 550 K. [This “Doppler-broadening” effect is commonly used to measure gas temperature, such as in astronomy.]
If an object is spherical with a radius of r when viewed at rest, how would its appearance change if it was traveling at relativistic speeds?
A Neutron is moving at a speed of 95% the speed of light, v= 0.95c
A)Calculate the Lorenz factor
B)Calculate the momentum of the neutron
C)Calculate the total energy
D)Calculate the K.E. of the neutron
Neutron mass = 1.675 x 10^(-27) kg
in order for a subatomic particle from space with a lifetime of τ in its own reference frame to reach the Earth’s surface, it must be able to travel a distance greater than or equal to the thickness of the atmosphere before it decays. If the thickness of the atmosphere i d in the Earth’s reference frame, find the minimum speed v at which this particle must travel in order to reach the Earth’s surface.
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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