WAve length

The wavelengths of k_{\alpha } and k_{\gamma } X- Rays are \lambda _{1} and \lambda _{2 } respectively. The wavelength of L _{\beta } X- Rays is
A) \frac{\lambda _{1 } + \lambda _{2}}{2} B) \frac{\mid \lambda _{1 } - \lambda _{2}\mid }{2} C) \frac{ \lambda _{1 } \lambda _{2} }{\lambda _{1 } - \lambda _{2}} D) \frac{ \lambda _{1 } \lambda _{2} }{\lambda _{1 } + \lambda _{2}}

1 Answers

29
govind ·

Kα is emitted for transition from 2 → 1 = λ1 Energy released = E1
Kγ is emitted for transition from 4 → 1 = λ2 Energy released = E2
Lβ is emitted for transition from 4 → 2 = λ3 Energy released = E3

So E2 = E3 + E1
E3 = E2 - E1
we know that E = hc/λ ..
hc/λ3 = hc/λ2 - hc/λ1
1/λ3 = 1/λ2 - 1/λ1
1/λ3 = λ1 - λ2 / λ1λ2

so λ3 = λ1λ2 / λ1 - λ2

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