Question

The ratio of energy of the electron in ground state of the hydrogen to electron in first excited state of ${He}^{+}$ is

• A. $1:4$
• B. $1:1$
• C. $1:8$
• D. $1:16$

Answer 1

The correct option is B $1:1$

Explanation:

The ratio of energy of the electron in ground state of the hydrogen to electron in first excited state of $H{e}^{+}$ is:

$Z=1$ for hydrogen

$Z=2$ for helium atom

$n=1$ for ground state of hydrogen

$n=2$ for excited state of helium atom

So, on putting these values in equation below :

$\frac{{z^2}_H}{{n^2}_H}\times \frac{{n^2}_{H{e}^{+}}}{{z^2}_{H{e}^{+}}}=\frac{1\times 4}{1\times 4}=1$

So ratio of the energy of the electron in ground state of the hydrogen to electron in first excited state of Helium ion is $1:1$

Option B is correct.