Question

Calculate the energy associated with the first orbit of $H{e}^{\oplus }$. What is the radius of orbit?

• A. 0.3026 nm
• B. 0.20645 nm
• C. 0.02645 nm
• D. 0.03026 nm

Answer 1

The correct option is C

0.02645 nm

Sol. $E_n$ = $-\frac{(2.18\times {10}^{-18}J)Z^2}{n^2}ato{m}^{-1}$

For $H{e}^{\oplus }$, $n$ = $1$, $Z$ = $2$

$E_1$ = $\frac{-(2.18\times {10}^{-18}J)\left(2^2\right)}{1^2}$

= $-8.72\times {10}^{-18}J$

The radius of the orbit is given:

$r_n=\frac{\left(0.0529nm\right)n^2}{Z}$

Since $n$ = 1, and $Z$ = $2$

$r_n$ = $\frac{\left(0.0529\right)\times 1^2}{2}$

= $0.02645nm$