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When an X-ray photon is scattered at 90° by a suitable material, its wavelength is
1. 0.048 Å
2. 0.012 Å
3. 0.024 Å
4. 0.0 Å

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Correct Answer - Option 3 : 0.024 Å

Concept:

Compton effect:

  • Compton effect is the term used for an unusual result observed when X-rays are scattered on some materials.
  • During the study, Compton found that wavelength is not dependent on the intensity of incident radiation.
  • It is dependent on the angle of scattering and on the wavelength of the incident beam.

Mathematically,

\( λ'-λ=\frac{h}{m_0c}\left(1-cosϕ\right)\)

Where, 

λ' = Wavelength after & Scattering,

λ = initial wavelength,

mo = rest mass of an electron = 9.109 × 10−31 kg,

c = speed of light = 3 × 108 m/s,

h = Planck's constant = 6.626×10−34 joule-sec,

ϕ = angle at which radiation scattered.

Calculation:

We know that,

\( λ'-λ=\frac{h}{m_0c}\left(1-cosϕ\right)\)

Given,

ϕ = 90∘ 

\(⇒ Δ λ = \frac{6.626\times 10^-34}{9.1\times 106-31 \times 3 \times 10^8}(1 - cos90^\circ )\)

⇒ Δλ = 0.024 Å 

Hence, the wavelength will be  0.024 Å.

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