A) \[{{Z}^{2}}{{n}^{2}}\]
B) \[\frac{{{Z}^{2}}}{{{n}^{2}}}\]
C) \[\frac{{{n}^{2}}}{Z}\]
D) \[\frac{{{Z}^{2}}}{n}\]
Correct Answer: C
Solution :
From Bohrs postulate the angular momentum of electron is \[mvr=\frac{nh}{2\pi }\] ?. (i) Also, the electrostatic force of attraction between the nucleus and electron is equal to centripetal force. \[\frac{m{{v}^{2}}}{r}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Ze\times e}{{{r}^{2}}}\] ? (ii) From Eqs. (i) and (ii), we get \[{{r}_{n}}={{n}^{2}}\frac{{{h}^{2}}{{\varepsilon }_{0}}}{\pi mZ{{e}^{2}}}\] \[\Rightarrow \] \[{{r}_{n}}\propto \frac{{{n}^{2}}}{Z}\]You need to login to perform this action.
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