/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 A radiation of energy \(E\) fall... [FREE SOLUTION] | 91影视

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Chapter 19: Problem 35

A radiation of energy \(E\) falls normally on a perfectly absorbing surface. The momentum transferred to the surface is (A) \(\frac{E}{c}\) (B) \(\frac{2 E}{c}\) (C) \(E c\) (D) \(\frac{E}{c^{2}}\)

Short Answer

Expert verified
The momentum transferred to the absorbing surface is given by the expression \(p = \frac{E}{c}\). So the correct answer is (A) \(\frac{E}{c}\).

Step by step solution

01

Understanding the principle of conservation of momentum

Since the radiation is perfectly absorbed by the surface, the momentum of the radiation is transferred to the absorbing surface. We can use the principle of conservation of momentum to analyze the situation.
02

Energy-momentum relation for a photon

The energy of a photon is related to its momentum through the following equation: \[E = p c\] where E is the energy of the photon, p is its momentum, and c is the speed of light.
03

Solve for the momentum

We are given the energy E of the radiation and we need to find the momentum transferred to the surface, which is equal to the momentum of the photon. Using the energy-momentum relation, we can solve for the momentum p: \[p = \frac{E}{c}\]
04

Compare the options with the solution

Now, we will compare the expression for the momentum we found with the options given in the question: (A) \(\frac{E}{c}\) - This matches our derived expression for the momentum. Therefore, this is the correct answer. (B) \(\frac{2E}{c}\) - This is not the correct expression for the momentum. (C) \(Ec\) - This is not the correct expression for the momentum. (D) \(\frac{E}{c^2}\) - This is not the correct expression for the momentum. The correct option is (A) \(\frac{E}{c}\).

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