An X-ray photon is found to have its wavelength doubled on being scattered through `90^(@)`. Find the energy of the incident photon:

Options

A. `8.1xx10^(-14)J`
B. `8.1xx10^(12)J`
C. `8.1xx10^(-10)J`
D. `8.1xx10^(-8)J`

Answer

A

Explanation

Compton change in wavelength is given by
`Delta lambda=(h)/(m_(0)c)(1-cos phi)`
when `theta=90^(@), Delta lambda= lambda` (wavelength is doubled)
Thus `lambda=(h)/(m_(0)c)=0*024Å`
Energy `hv=(hc)/(lambda)=(hc)/(h//m_(0)c)=m_(0)c^(2)`
`=(9*0xx10^(-31)xxkgxx3*0xx10^(8) m//"sec")^(2)`
`=8*1xx10^(-14)J`