Question

What is the energy of state in a triply ionised berrylium $\left(B{e}^{+++}\right)$ whose radius is equal to that of ground state of hydrogen?

• A. 27.2 eV
• B. 54.4 eV
• C. 13.6 eV
• D. 40.8 eV

Answer 1

The correct option is B 54.4 eV

$r_1=r_2,\frac{Z_1}{Z_2}={\left(\frac{n_1}{n_2}\right)}^{2}Asr\alpha \left(\frac{n^2}{z}\right)$
$\frac{1}{4}={\left(\frac{1}{n_2}\right)}^2$
$n_2=2$
$E=-13.6\frac{z^2}{n^2}$
$E=-13.6\times \frac{4^2}{2^2}$
$=-13.6\times 4$
$=54.4eV$