Concept explainers
(a)
The energy and momentum of one laser photon if the laser wavelength is
(a)
Answer to Problem 93P
The energy of the photon is
Explanation of Solution
Write the equation for the energy of the photon.
Here,
Write the equation for the energy of the momentum of the photon in terms of energy.
Here,
Rewrite the above equation for
Conclusion:
The value of
Substitute
Substitute
Therefore, the energy of the photon is
(b)
The number of photons per second emitted by the laser.
(b)
Answer to Problem 93P
The number of photons per second emitted by the laser is
Explanation of Solution
The number of photons per second emitted by the laser is given by the ratio of power of the laser to the energy per photon.
Write the equation for the rate of photon emission.
Conclusion:
Given that the output power of the laser pointer is
Substitute
Therefore, number of photons per second emitted by the laser is
(c)
The average force on the laser due to the momentum carried away by the emitted photons.
(c)
Answer to Problem 93P
The average force on the laser due to the momentum carried away by the emitted photons is
Explanation of Solution
The impulse momentum theorem states that the impulse is equal to the change in momentum. The impulse is the product of the average force applied and the time interval during which the force acts.
Write the mathematical expression for the impulse-momentum theorem.
Here,
Rewrite the above equation for
Use equation (II) to write the expression for the change in momentum.
Write the equation for
Put equations (V) and (VI) in equation (IV).
Conclusion:
Substitute
Therefore, the average force on the laser due to the momentum carried away by the emitted photons is
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