A) \[\frac{1}{n},\frac{1}{{{n}^{2}}},{{n}^{2}}\]
B) \[\frac{1}{n},{{n}^{2}},\frac{1}{{{n}^{2}}}\]
C) \[{{n}^{2}},\frac{1}{{{n}^{2}}},{{n}^{2}}\]
D) \[n,\frac{1}{{{n}^{2}}},\frac{1}{{{n}^{2}}}\]
Correct Answer: A
Solution :
According to Booths theory of hydrogen atom (i) The speed of electron in nth orbit \[{{v}_{n}}=\frac{Z{{e}^{2}}}{2{{\varepsilon }_{0}}nh}\] or \[{{v}_{n}}\propto \frac{1}{n}\] (ii) The energy of electron in the nth orbit \[{{E}_{n}}-\left( \frac{m{{e}^{4}}}{8\varepsilon _{0}^{2}{{h}^{2}}} \right).\,\frac{{{Z}^{2}}}{{{n}^{2}}}=-13.6\frac{{{Z}^{2}}}{{{n}^{2}}}eV\] or \[{{E}_{n}}\propto \frac{1}{{{n}^{2}}}\] (iii) The radius of the electron in the nth orbit \[{{r}_{n}}=\frac{{{n}^{2}}{{h}^{2}}{{\varepsilon }_{0}}}{\pi mZ{{e}^{2}}}=0.53\frac{{{n}^{2}}}{2}\overset{o}{\mathop{A}}\,\] So, option is correct.
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