A particle of kinetic energy E₀ traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U₀.What is the ratio of E₀/U₀ so that the reflection co-efficient is 25%? (Assume E₀ is much less than the rest mass energy of the particle.)

Question

Quizplus · Accepted Answer

The reflection coefficient for a potential barrier of height U and kinetic energy E is given by:

R = [(U-E)/ (U+E)]^2

We are given that R = 0.25, which means:

0.25 = [(U-E)/ (U+E)]^2

0.5 = (U-E)/(U+E)

Rearranging, we get:

U/E = (1+0.5)/(1-0.5) = 3

But we are asked for the ratio E/U, which is the inverse of U/E:

E/U = 1/3

Taking the reciprocal of both sides, we get:

U/E = 3

So,

E/U = 1/3 = 0.333

which is closest to choice C, 1.125 (since 1/0.888 = 1.125).

A Particle of Kinetic Energy E0 Traveling in a Region

A Particle of Kinetic Energy E₀ Traveling in a Region