Question

The energies of an electron in first orbit of $He^{+}$ and in third orbit of $Li^{2+}$ 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 $\left( He ^{+}\right)$

$ 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 $\left( Li ^{2+}\right)$

$Z=3, n=3$

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

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