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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main · Physics · Electromagnetic Waves

In compton scattering process, the incident X -radiation is...

In compton scattering process, the incident XX-radiation is scattered at an angle 60∘60^{{}^{{}^{\circ}}}. The wavelength of the scattered radiation is 0.22A˚0.22 Å. The wavelength of the incident XX-radiation in A˚Å units is

Options

  1. A0.5080.508
  2. B0.4080.408
  3. C0.2320.232
  4. D0.2080.208

Correct answer

D. 0.2080.208

Step-by-step solution

For Compton effect we have the relation
λ2−λ1=hm0c(1−cos⁡θ)\lambda_2-\lambda_1=\frac{h}{m_0 c}(1-\cos \theta)
λ1=\lambda_1= wavelength of incident radiation
λ2=\lambda_2= wavelength of scattered radiation
<br/>∴0.22−λ1=0.024(1−cos⁡60)<br/>0.22−λ1=0.024(1−12)<br/>0.22−λ1=0.024×12<br/>λ1=0.22−0.012=0.208A˚<br/>\begin{aligned}<br/>\therefore 0.22-\lambda_1 & =0.024(1-\cos 60) \\<br/>0.22-\lambda_1 & =0.024\left(1-\frac{1}{2}\right) \\<br/>0.22-\lambda_1 & =0.024 \times \frac{1}{2} \\<br/>\lambda_1 & =0.22-0.012=0.208 Å<br/>\end{aligned}
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