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Chapter 38: Q31P (page 1182)

What percentage increase in wavelength leads to a 75 % loss of photon energy in a photon-free electron collision?

Short Answer

Expert verified

300 %

Step by step solution

01

Identification of the given data

The given data is listed below as-

There is a 75 % loss of photon energy

02

Significance of the momentum of a photon

The momentum of a photon is related to its energy and is given by-

p=Ec

Here, E is the rest energy of a photon which is given byE=mec2.

me Is the mass of electron and is the speed of light.

03

To find the percentage increase in wavelength

Let E is the energy of photon initially andE'is the energy of photon after collision. The fractional energy loss is given by-

ΔEE=E−E'E=Δλλ+Δλ

Now,

Δλλ=ΔE/E1−ΔE/E=0.751−0.75=3=300 %

Thus, the percentage increase in wavelength is 300 %.

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Most popular questions from this chapter

Electrons accelerated to an energy of 50 GeVhave a de Broglie wavelength λsmall enough for them to probe the structure within a target nucleus by scattering from the structure. Assume that the energy is so large that the extreme relativistic relation p=Ecbetween momentum magnitude pand energy Eapplies. (In this extreme situation, the kinetic energy of an electron is much greater than its rest energy.)

(a) What is λ?

(b) If the target nucleus has radius R=5.0 fm, what is the ratio Rλ?

Neutrons in thermal equilibrium with matter have an average kinetic energy of (3/2)kT, where is the Boltzmann constant and T, which may be taken to be 300K, is the temperature of the environment of the neutrons. (a) What is the average kinetic energy of such a neutron? (b) What is the corresponding de Broglie wavelength?

In an old-fashioned television set, electrons are accelerated through a potential difference of 25.0kV. What is the de Broglie wavelength of such electrons? (Relativity is not needed.)

A bullet of mass travels at1000m/s . Although the bullet is clearly too large to be treated as a matter wave, determine what Eq. 38-17 predicts for the de Broglie wavelength of the bullet at that speed.

Consider a balloon filled with helium gas at room temperature and atmospheric pressure. Calculate (a) the average de Broglie wavelength of the helium atoms and (b) the average distance between atoms under these conditions. The average kinetic energy of an atom is equal to 3/2kT, wherek is the Boltzmann constant. (c) Can the atoms be treated as particles under these conditions? Explain.
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