Concept explainers
(a)
Find the speed of proton.
(a)

Answer to Problem 28P
The speed of proton is
Explanation of Solution
The proton is accelerated energy is
Write the equation for relativistic energy.
Here,
Rearrange the above equation to get the
Conclusion:
Substitute
Therefore, the speed of proton is
(b)
Find time it would take proton to make one rotation.
(b)

Answer to Problem 28P
The time taken by proton to make one rotation is
Explanation of Solution
The circumference of tunnel is
Write the relativistic equation to find time take by proton.
Here, the
Conclusion:
Substitute
Therefore, the time taken by proton to take on rotation is
(c)
Find time it would take proton to make one rotation in the reference frame.
(c)

Answer to Problem 28P
The time taken by proton to make one rotation in reference frame is
Explanation of Solution
Write the equation for time taken by proton in reference frame.
Here,
Conclusion:
Substitute
Therefore, the time taken by proton to make one rotation in reference frame is
(d)
Find the de Broglie wavelength of proton.
(d)

Answer to Problem 28P
The de Broglie wavelength of proton is
Explanation of Solution
Write the relativistic de Broglie equation.
Here,
Conclusion:
Substitute
Therefore, the de Broglie wavelength of proton is
(e)
Find the mosquito’s speed.
(e)

Answer to Problem 28P
The mosquito’s speed is
Explanation of Solution
First the decision has to be made whether to use relativistic or nonrelativistic formula.
Write the kinetic energy in joules,
The rest energy of mosquito is given below,
Therefore, the rest energy of mosquito is much higher than the kinetic energy, thus the nonrelativistic equation must be used to calculate the speed.
Write the nonrelativistic equation for speed.
Here,
Rewrite the above equation to find speed.
Here,
Conclusion:
Substitute
Therefore, the mosquito’s speed is
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Chapter 30 Solutions
PHYSICS
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