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An X-ray source of unknown wavelength is directed at a carbon sample. An electron is scattered with a speed of4.5×107m/s at an angle of.Determine the wavelength of the X-ray source.

Short Answer

Expert verified

The Wavelength of the X-ray source directed at the carbon sample is 0.213 nm.

Step by step solution

01

Concept Introduction

The expression for the Compton scattering can be expressed as,

λ'-λ=hmec(1-cosθ)

02

Analysis of given data and arriving at the scattered wavelength.

According to the given data, the scattered electron has a speed of,

v=4.5×107m/s

We know that KE=12mv2

And also for the scattered electron of λ',KE=hcλ'

Thus,

role="math" localid="1659080762269" 12mv2=hcλ'λ'=2hcmv2λ'=2×6.625×10-34J·s3×108m/s9.1×10-31kg×4.5×107m/s2λ'=21.5×10-m

03

Using the Compton effect equation.

We have,

λ=λ'-hmc1-cosθλ=21.5×10-11m-625×10-34J·s9.1×10-31kg×3×108m/s1-cosθλ=21.5×10-11m-0.242×10-11m×05λ=21.379×10-11λ=0.213nm

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Most popular questions from this chapter

Compton used X-rays of 0.071nm wavelength. Some of the carbon’s electrons are too tightly bound to be stripped away by these X-rays, which accordingly interact essentially with the atom as a whole. In effect mein equation (3-8) is replaced by carbon’s atomic mass. Show that this explains why some X-rays of the incident wavelength were scattered at all angles.

An electron moving to the left at 0.8c collides with an incoming photon moving to the right . After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?

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  1. Assuming that the massive object is moving slowly, so that non-relativistic formulas are valid, find in terms of m , p and c the ratio of the massive object’s kinetic energy, and argue that it is small.
  2. Find the ratio found in part (a), but using relativistically correct fomulas for the massive object. (Note: E2=p2c2+m2c4may be helpful.)
  3. Show that the low-speed limit of the ratio of part (b) agrees with part (a) and that the high-speed limit is 1.
  4. Show that at very high speed, the kinetic energy of a massive object approaches .

A low-intensity beam of light is sent toward a narrow single slit. On the far side, individual flashes are seen sporadically at detectors over a broad area that is orders of magnitude wider than the slit width. What aspects of the experiment suggest a wave nature for light, and what aspects suggest a particle nature?

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