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  • X-rays of wavelength are scattered from a target. The wavelength of the X-rays scattere

X-rays of wavelength 10.0 \mathrm{pm} are scattered from a target. The wavelength of the X-rays scattered through 30^{\circ} is:
 

Option: 1

10.32 \mathrm{pmn}
 


Option: 2

12 \mathrm{pm}
 


Option: 3

10 \mathrm{~nm}

 


Option: 4

\mathrm{10 \AA}


Answers (1)

best_answer

The change in wavelength is given by

\mathrm{ \Delta \lambda=\lambda^{\prime}-\lambda=\frac{\mathrm{h}}{\mathrm{m}_0 \mathrm{c}}(1-\cos \phi) }

Where, \lambda^{\prime}= wavelength of the \mathrm{X}-rays scattered

and \mathrm{\lambda_{\mathrm{c}}=\frac{\mathrm{h}}{\mathrm{m}_0 \mathrm{c}}= compton \: wavelength =2.426 \times 10^{-12} \mathrm{~m}}

\mathrm{\Rightarrow \lambda^{\prime}=\lambda+\lambda_{\mathrm{c}}\left(1-\cos 30^{\circ}\right)=10 \mathrm{pm}+0.134 \lambda_{\mathrm{c}}=10.32 \mathrm{pm}}

Hence option 1 is correct.
 

Posted by

Ajit Kumar Dubey

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