Question

Calculate the radius of the third orbit of a single electron species, if the energy of this orbit is $-13.6\mathrm{eV}.$

• A. $1.58\mathrm{\AA }$
• B. $0.529\mathrm{\AA }$
• C. $1058\mathrm{\AA }$
• D. $2096\mathrm{\AA }$

Answer 1

The correct option is A

$1.58\mathrm{\AA }$

Explanation for correct option: (A)

The energy of the orbital is calculated by the following formula,

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

Substitute the known values,

$-13.6\mathrm{eV}=-\frac{13.6\times Z^2}{3^2}\mathrm{eV}/\mathrm{atom}$

or

$Z=3$

The radius of nth orbit is calculated by the following formula,

$r_n=\frac{0.529\times n^2}{Z}\mathrm{\AA }$

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

Substitute the values,

$\begin{array}{ccc}{r}_n& =& \frac{0.529\times 3^2}{3}\mathrm{\AA }\\ & =& 1.58\mathrm{\AA }\end{array}$

Hence, the correct option is (A).