X-rays of wavelength 22 pm are scattered from a carbon target. The scattered radiation is being viewed at 85 degrees to the incident beam. What is Compton's shift? (Answer: 2.2 ｘ 10⁻¹² m)



Given:

Wavelength of X-ray = λ =  22 pm = 22 ｘ 10⁻¹² m

Scattering angle = ፀ = 85°

∴ Plank's Constant = h =  6.626 ｘ 10⁻³⁴ m² kg s⁻¹

∴ Rest mass of the electron = m₀ = 9.11 ｘ 10⁻³¹ kg

∴ Speed of light = 3 ｘ 10⁸ m s⁻¹


To Find:

Compton Shift  = Δλ =  ?



Solution:

Since we have

Δλ =    `\frac {h}{m₀c}` (1 - cosፀ)

By putting values

Δλ =    `\frac {6.626 ｘ 10⁻³⁴ m² kg s⁻¹}{9.11 ｘ 10⁻³¹ kg ｘ 3 ｘ 10⁸ m s⁻¹ }` (1 - cos 85°)


Δλ =    `\frac {6.626 ｘ 10⁻³⁴ m² kg s⁻¹}{27.3 ｘ 10⁻²³ kg m s⁻¹ }` (1 - 0.0872)

Δλ =   0.242  ｘ 10⁻¹¹ ｘ 0.913 m

Δλ =   2.2  ｘ 10⁻¹² m  -----------------Ans.



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