Question

I What is the radius of a hydrogen atom whose electron is bound by$0.378\mathrm{eV}$ ?

Short answer

$r_6=1.9\mathrm{nm}$

Step-by-step solution

Given information

We can start the solution with expression for energy in nth state for hydrogen atom

Calculation

$E_n=-\frac{13.6\left(\mathrm{eV}\right)}{n^2}$

$n^2=-\frac{13.6\left(\mathrm{eV}\right)}{E_n}$ (Express $n^2$)

localid="1650738237508" $n=\sqrt{\frac{-13.6\left(\mathrm{eV}\right)}{-0.378\left(\mathrm{et}\right)}}$((-)sign of $E_n$because energy in any atom is negative)

$n\approx 6$

localid="1650739244089" $r_n\left.=n^2{a}_B\text{(radiusisnthstate}\right)$

$r_6=1.9\mathrm{nm}$