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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