Chapter 3: Q34E (page 94)

An X-ray source of unknown wavelength is directed at a carbon sample. An electron is scattered with a speed of $4.5 \times 10^{7} m / s$ 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

Concept Introduction

The expression for the Compton scattering can be expressed as,

$λ' - λ = \frac{h}{m_{e} c} (1 - c o s θ)$

Analysis of given data and arriving at the scattered wavelength.

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

$v = 4.5 \times 10^{7} m / s$

We know that $K E = \frac{1}{2} m v^{2}$

And also for the scattered electron of $λ', K E = \frac{h c}{λ'}$

Thus,

role="math" localid="1659080762269" $\frac{1}{2} m v^{2} = \frac{h c}{λ'} λ' = \frac{2 h c}{m v^{2}} λ' = \frac{2 \times (6.625 \times 10^{- 34} J \cdot s) (3 \times 10^{8} m / s)}{(9.1 \times 10^{- 31} k g) \times {(4.5 \times 10^{7} m / s)}^{2}} λ' = 21.5 \times 10^{-} m$

Using the Compton effect equation.

We have,

$λ = λ' - \frac{h}{m c} (1 - \cos θ) λ = 21.5 \times 10^{- 11} m - \frac{625 \times 10^{- 34} J \cdot s}{(9.1 \times 10^{- 31} k g) \times 3 \times 10^{8} m / s} (1 - \cos θ) λ = 21.5 \times 10^{- 11} m - (0.242 \times 10^{- 11} m \times (05)) λ = 21.379 \times 10^{- 11} λ = 0.213 n m$

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An X-ray source of unknown wavelength is directed at a carbon sample. An electron is scattered with a speed of $4.5 \times 10^{7} m / s$ at an angle of.Determine the wavelength of the X-ray source.

Short Answer

Step by step solution

Concept Introduction

Analysis of given data and arriving at the scattered wavelength.

Using the Compton effect equation.

One App. One Place for Learning.

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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

Step by step solution

Concept Introduction

Analysis of given data and arriving at the scattered wavelength.

Using the Compton effect equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Space Physics

Fields in Physics

Rotational Dynamics

Conservation of Energy and Momentum

Energy Physics

Study anywhere. Anytime. Across all devices.

An X-ray source of unknown wavelength is directed at a carbon sample. An electron is scattered with a speed of $4.5 \times 10^{7} m / s$ at an angle of.Determine the wavelength of the X-ray source.