A) \[\sqrt{\left( \frac{2mc}{h} \right)}{{\lambda }_{1}}\]
B) \[\sqrt{\frac{h}{2mc}}\times {{\lambda }_{1}}\]
C) \[\left( \frac{2mc}{h} \right)\times \lambda _{1}^{2}\]
D) None
Correct Answer: C
Solution :
[c] As K.E of emitted \[{{e}^{-}}\] = energy of x-Ray \[\frac{1}{2}m{{V}^{2}}=hv\] \[\frac{{{P}^{2}}}{2m}=\frac{hc}{\lambda }\] \[\therefore P=\sqrt{\frac{2mhc}{\lambda }}\] \[\therefore {{\lambda }_{1}}=\frac{h}{p}=\frac{h}{\sqrt{\frac{2mhc}{\lambda }}}=\sqrt{\frac{h\lambda }{2mc}}\] Or \[{{\lambda }_{1}}^{2}=\frac{h\lambda }{2mc}\] Or \[\lambda =\left( \frac{2mc}{h} \right){{\lambda }_{1}}^{2}\]
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