What is the amount of energy associated with first orbit of monopositive helium ion?…
What is the amount of energy associated with first orbit of monopositive helium ion? $\left[\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}\right]$
$-1.9 \times 10^{-18} \mathrm{~J}$
$-4.36 \times 10^{-18} \mathrm{~J}$
$\quad-6.54 \times 10^{-18} \mathrm{~J}$
$-8.72 \times 10^{-18} \mathrm{~J}$
Solution
For the first orbit of monopositive $\mathrm{He}^{+}$ion, $\mathrm{Z}=2, \mathrm{n}=1$
$\begin{aligned}
& E_n=-2.18 \times 10^{-18}\left(\frac{Z^2}{n^2}\right) J \\
& E_1=-2.18 \times 10^{-18}\left(\frac{2^2}{1^2}\right)=4 \times 2.18 \times 10^{-18}
\end{aligned}$
$\therefore \quad \mathrm{E}_1=-8.72 \times 10^{-18} \mathrm{~J}$