Question

Calculate the energy and radius of He+ ion? ​

Answer 1

$\textsf{\underline {\Large {Structure of the atom}}}$ :

Energy of an electron in nth orbit

$\boxed{\mathsf{E_n\:=\:{\dfrac{-\:2.18{\times{{10}^{-18}}}\:{Z}^{2}}{{n}^{2}}J \:/atom}}}$

↪️ For first orbit of $\mathsf{{He} ^{+}}$,

Z = 2, n = 1

$\mathsf{E_1\:=\:{\dfrac{-\:2.18{\times{{10}^{-18}}}\:* \:{2}^{2}}{{1}^{2}}J \:/atom}}$

➡️ $\boxed{\mathsf{E_1\:=\:-\:8.72\:{\times{{10}^{-18}}}\:J}}$

↪️Radius of nth orbit,

$\boxed{\mathsf{r_n\:=\:{\dfrac{0.0529\:{n}^{2}}{Z}\:nm}}}$

$\mathsf{r_1\:=\:{\dfrac{0.0529\:*\:{1}^{2}}{2}\:nm}}$

➡️ $\boxed{\mathsf{r_1\:=\:0.02645\:nm}}$