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 $Li^{+}$ ?

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

Answer 1

Answer: (A)

$4 : 9$

Answer 2

$\because E_{n} \propto \frac{Z^{2}}{n^{2}}$

For $H$ atom $E_{1} \propto \frac{1^{2}}{1^{2}} [\because Z=1$ for hydrogen $]$

or $E_{1} \propto 1$

For $Li ^{+}$ ion $: E_{2} \propto \frac{(3)^{2}}{(2)^{2}} \left[\because Z=3\right.$ for $Li ^{+}$ ion $]$

or $E_{2} \propto \frac{9}{4}$

Thus, $E_{1}($ for $H$ atom $): E_{2}\left(\right.$ for $Li ^{+}$ ion $)$

or $1: \frac{9}{4}$ or $4: 9$