Question

The energies of an electron in first orbit of $H{e}^{+}$ and in third orbit of $L{i}^{2+}$ in $J$ are respectively

• A. $-8.72\times 10^{-18},-2.18\times 10^{-18}$
• B. $-8.72\times 10^{-18},-1.96\times 10^{-17}$
• C. $-1.96\times 10^{-17},-2.18\times 10^{-18}$
• D. $-8.72\times 10^{-17},-1.96\times 10^{-17}$

Answer 1

Answer: (A)

Use relation:

$E_n=-2.18\times 10^{-18}\cdot \frac{Z^2}{n^2}J/ion$

where,

$E_n=$ energy of an electron in $n$ th orbit

$Z=$ atomic number,

$n=$ orbit number

For helium ion $\left(H{e}^{+}\right)$

$Z=2,n=1$

$\therefore E_n=-2.18\times 10^{-18}\times \frac{2^2}{1^2}$

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

For lithium ion $\left(L{i}^{2+}\right)$

$Z=3,n=3$

$\therefore E_n=-2.18\times 10^{-18}\times \frac{3^2}{3^2}$

$=-2.18\times 10^{-18}J$