Question

Which one of the following represents the correct ratio of the energy, of electron in ground state of H atom to that of the electron in the first excited state of $L{i}^{+}$ ?

• A. 4 : 9
• B. 9 : 4
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is A 4 : 9

$\because E_n\propto \frac{Z^2}{n^2}$For H atom $E_1\propto \frac{1^2}{1^2}$ [$\because Z=1$ for hydrogen ]
Or $E_1\propto 1$
For $L{i}^{+}$ ion : $E_2\propto \frac{(3{)}^2}{(2{)}^2}$ [$\because z=3$ for $L{i}^{+}$ ion]
Or $E_2\propto \frac{9}{4}$
Thus, $E_1$ (for Harmon) : $E_2$ (for $L{i}^{+}$ ion)
Or $1:\frac{9}{4}$ or $4:9$