A) \[{{n}^{2}}\]
B) n
C) \[\sqrt{n}\]
D) None of these
Correct Answer: C
Solution :
| relation between potential energy and kinetic energy of electron, |
| \[\operatorname{P}.E=-2K.E\] |
| \[-\frac{1}{2}\times P.E.=K.E\] |
| \[-\frac{1}{2}\left( -\frac{1}{2}{{\operatorname{mkr}}^{2}} \right)=\frac{1}{2}{{\operatorname{mv}}^{2}},\] |
| \[\frac{1}{2}{{\operatorname{kr}}^{2}}={{\operatorname{v}}^{2}}..(i)\] |
| As we know,\[\operatorname{mvr}=\frac{\operatorname{nh}}{2\pi }\] |
| \[\therefore \,{{\operatorname{v}}^{2}}=\frac{{{\operatorname{n}}^{2}}{{h}^{2}}}{4{{\pi }^{2}}{{\operatorname{m}}^{2}}{{r}^{2}}}\] |
| Put this value in equation (i); |
| \[{{\operatorname{r}}^{4}}=\frac{{{n}^{2}}{{h}^{2}}}{2{{\pi }^{2}}{{\operatorname{m}}^{2}}K}\] |
| \[\operatorname{or}\,r\propto \sqrt{\operatorname{n}}\] |
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