Question

In a hydrogen atom, the first Bohr's orbit has radius $0.53\mathring{A}$. The potential at any point on the orbit to nuclear charge is:

• A. $5.23V$
• B. $11.32V$
• C. $18.96V$
• D. $27.17V$

Answer 1

The correct option is D $27.17V$

$\begin{array}{c}\text{we know,}\\ \text{radius}\left(r\right)=\frac{0.529n^2}{z}\end{array}$

$\begin{array}{c}\begin{array}{c}\text{for bohrs radius}n=1\\ z=1\text{(hydrogen)}\\ r=0.53\dot{A}\end{array}\end{array}$

$\begin{array}{c}\text{Now}\\ \text{Potential Energy}=\frac{27.17n^2}{z^2}\text{ev}\\ \text{for}n=1\text{and}z=1\\ PE=\frac{27.77(1{)}^2}{(1{)}^2}\\ PE=27.17eV\end{array}$

$\frac{PE}{\text{nuclear change}}=27.17Volt$