Question

When hydrogen atom is in its first excited level, its radius is :

• A. four times, its ground state radius
• B. twice, its ground state radius
• C. same as its ground state radius
• D. half of its ground state radius

Answer 1

Answer: (A)

Key Idea: The radius of nth Bohrs orbit of hydrogen atom $ {{r}_{n}}=\frac{{{\varepsilon }_{0}}{{n}^{2}}{{h}^{2}}}{\pi m\,{{e}^{2}}} $ As per key idea, $ {{r}_{n}}={{n}^{2}}{{a}_{0}} $ or $ {{r}_{n}}\propto {{n}^{2}} $ For ground state, $ n=1 $ For first excited state, $ n=2 $ $ \therefore $ $ \frac{{{r}_{2}}}{{{r}_{1}}}={{\left( \frac{2}{1} \right)}^{2}}=4 $ or $ {{r}_{2}}=4{{r}_{1}} $ Therefore, radius of first excited state is 4-times than that of ground state radius in H-atom.