Question

If the energy of the second orbit of a single electron species is $-x\mathrm{eV},$ then calculate the atomic number of that atom in terms of $x.$

• A. $2x\sqrt{\frac{1}{13.6}}$
• B. $2\sqrt{\frac{x}{13.6}}$
• C. $\sqrt{\frac{2x}{13.6}}$
• D. $\frac{2x}{13.6}$

Answer 1

The correct option is B

$2\sqrt{\frac{x}{13.6}}$

Explanation for correct option: (B)

The energy of an orbital $\left(E_n\right)$ is formulated as

$E_n=\frac{13.6\times Z^2}{n^2}\mathrm{eV}/\mathrm{atom}$

Here, n is the orbit number and Z is the atomic number.

Substitute the known values,

$$\begin{gathered} \begin{array}{ccc}-x\mathrm{eV}& =& -\frac{13.6\times Z^2}{2^2}\mathrm{eV}/\mathrm{atom}\\ Z& =& \sqrt{\frac{4x}{13.6}}\end{array} \\ =2\sqrt{\frac{x}{13.6}} \end{gathered}$$

Therefore, the atomic number of that atom in terms of $x$ is $2\sqrt{\frac{x}{13.6}}.$

Hence, the correct option is B.