When an electron in an excited state of Mo atom falls L to K -shell, an X -ray is emitted. These X -rays are diffranted at angle of ` 7.75^(@)` by planes with a sepration of 2.64Å . What is the difference in energy between K-shelll and L -shell in Mo, assuming a first order diffraction ? ` ( sin 7.75^(@) = 0.1349)

Options

A. `26.88 xx 10^(-16) J`
B. `25.27 xx 10^(-15) J`
C. `27.88 xx 10^(-16) J`
D. none of these

Answer

C

Explanation

`2a sin theta = n lamda`
`lamda = 2a sin theta = 2 xx 2.64 xx 10^(-10) xx sin 7.75^@`
` = 0.7123 xx 10^(-10) m`
` E = (hc)/(lamda)`
` = (6.62 xx 10^(-34) xx 3 xx 10^8)/(0.7123 xx 10^(-10)) = J = 27.88 xx 10^(-16) J`