A) \[{{\lambda }_{p}}\propto \lambda _{e}^{2}\]
B) \[{{\lambda }_{p}}\propto {{\lambda }_{e}}\]
C) \[{{\lambda }_{p}}\propto \sqrt{{{\lambda }_{e}}}\]
D) \[{{\lambda }_{p}}\propto \frac{1}{\sqrt{{{\lambda }_{e}}}}\]
Correct Answer: A
Solution :
[a] Wavelength of electron, \[{{\lambda }_{e}}=\frac{h}{\sqrt{2mE}}\] and proton\[{{\lambda }_{p}}=\frac{hc}{E}\] \[\Rightarrow \]\[\lambda _{e}^{2}=\frac{{{h}^{2}}}{2mE}\]or\[E=\frac{hc}{{{\lambda }_{p}}}\] \[\therefore \]\[\lambda _{e}^{2}=\frac{{{h}^{2}}}{2m.\frac{hc}{{{\lambda }_{p}}}}\Rightarrow \lambda _{e}^{2}=\frac{{{h}_{2}}}{2mhc}{{\lambda }_{p}}\] \[\Rightarrow \] \[\lambda _{e}^{2}\propto {{\lambda }_{p}}\]
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