• # question_answer                 Bohr radius for the hydrogen atom (n = 1) is approximately 0.530 $\overset{\text{o}}{\mathop{\text{A}}}\,$. The radius for the first excited state (n = 2) orbit is (in $\overset{\text{o}}{\mathop{\text{A}}}\,$): A)                                                                                                                                                                                                                 0.13 B)                 1.06        C)                            4.77        D)                                            2.12

$r\propto \,n_{1}^{2}\,{{Z}^{2}}$                 where n = number of orbit                 Z = Atomic number                 $\because$     ${{r}_{1}}\propto n_{1}^{2}$                 ${{r}_{2}}\propto \,n_{2}^{2}\,(Z=1\,for\,H-atom)$                 $So,\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{n_{1}^{2}}{n_{2}^{2}}$                 $\frac{0.530}{{{r}_{2}}}=\frac{{{1}^{2}}}{{{2}^{2}}}$                 $\therefore {{r}_{2}}=0.530\times 4=2.120\,{\AA}$