Question

From the following energy levels of hydrogen atom, the values of $E_{\infty}$ and $E_{3}$ in $J$ are, respectively
____ $E_{\infty}=\ldots \ldots \ldots$
____ $E_{3}=\ldots \ldots \ldots$
____ $E_{2}=-0.545 \times 10^{-18}\, J$
____ $E_{1}=-2.18 \times 10^{-18} \,J$

• A. $1,-0.242 \times 10^{-18}$
• B. $\infty,-0.726 \times 10^{-18}$
• C. $0,-0.242 \times 10^{-18}$
• D. $0,-0.321 \times 10^{-18}$

Answer 1

Answer: (C)

$ E_{n}=-2.18 \times 10^{-18} \cdot \frac{Z^{2}}{n^{2}}$

where, $E_{n}=$ energy of an electron in $n$ th orbital.

$Z=$ atomic number

$n=$ number of orbital

For hydrogen, $Z=1$

Therefore,

$E_{3} =-2.18 \times 10^{-18} \times \frac{1}{3^{2}} $

$=-\frac{2.18 \times 10^{-18}}{9} $

$=-0.242 \times 10^{-18}$

and $E_{\infty}=-2.18 \times 10^{-18} \times \frac{1}{\infty}$

$E_{\infty}=0$

Hence, $E_{\infty}=0$ and $E_{3}=-0.242 \times 10^{-18}\, J$