Question

The ratio of areas of the electron orbits for the first excited state and the ground state for the hydrogen atom is

• A. 4 : 1
• B. 16 : 1
• C. 8 : 1
• D. 2 : 1

Answer 1

The correct option is B 16 : 1

The radius of the orbit of the electron in the nth excited state
$r_e=\frac{n^{2}4\pi {\epsilon }_0{h}^2}{4{\pi }^{2}mZ{e}^2}$
For the first excited state
$n=2,z=1$
$\because r^{\prime }=\frac{4{\epsilon }_0{h}^2}{\pi m{e}^2}$
For the ground state of hydrogen atom
$n-1,Z=1$
$\because r^{\prime }=\frac{h^2{\epsilon }_0}{\pi m{e}^2}$
The ratio of radius
$\frac{r^{\prime }}{r^{\prime \prime }}=\frac{4}{1}$
The ratio of area of the electron orbit for hydrogen atom
$\frac{A^{\prime }}{A^{\prime \prime }}=\frac{4\pi \left(r^{\prime }\right)}{4\pi (r^{\prime \prime }{)}^2}$
$\frac{A^{\prime }}{A^{\prime \prime }}=\frac{16}{1}$