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 $r_n=\frac{{\epsilon }_0{n}^2{h}^2}{\pi m{e}^2}$ 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 $r_2=4r_1$ Therefore, radius of first excited state is 4-times than that of ground state radius in H-atom.