Question

calculate the energy and radius of 2nd orbit to He+ ion

Answer 1

Energy = -13.6Z²/n²
= -13.6 * 4/4
= -13.6 eV

Radius = 0.529 n²/Z Å
= 0.529 * 4/2
= 1.058 Å

Answer 2

Answer : The energy and radius of second orbit of $He^+$ ion are, -13.6 ev and 105.8 pm respectively.

Solution :

Formula used for energy of $n^{th}$ orbit of $He^+$ ion or hydrogen like atom will be,

$E_n=-13.6\times \frac{Z^2}{n^2}ev$

Formula used for the radius of the $n^{th}$ orbit will be,

$r_n=\frac{n^2\times 52.9}{Z}pm$   (in pm)

where,

$E_n$ = energy of $n^{th}$ orbit

$r_n$ = radius of $n^{th}$ orbit

n = number of orbit

Z = atomic number

Now we have to calculate the energy and radius of second orbit of $He^+$ ion.

$E_2=-13.6\times \frac{(2)^2}{(2)^2}ev=-13.6ev$

$r_2=\frac{(2)^2\times 52.9}{2}pm=105.8pm$

Therefore, the energy and radius of second orbit of $He^+$ ion are, -13.6 ev and 105.8 pm respectively.