Question

Energy of an electron in the second orbit of hydrogen atom is E and the energy of electron in 3rd orbit of He will be

Answer 1

Given :

Energy of an electron  in 2nd orbit of Hydrogen :

=  E

To Find :

Energy of electron in 3rd orbit of Helium = ?

Solution :

∴We know that the energy of an electron in the orbit of an atom is directly proportional to   $\frac{Z^{2}}{n^{2} }$

i.e.  Energy    $\alpha$   $\frac{Z^{2}}{n^{2} }$

Or , Energy $= \frac{kZ^{2}}{n^{2} }$

where z is atomic no. , n is the orbit in which electron is present and k is constant.

So,  E$= \frac{k1^{2}}{2^{2}} = \frac{k}{4}$

Now the energy of electron in 3rd orbit of He atom is :

$= \frac{k2^{2}}{3^{2}}\\ \\=\frac{k}{4}\times \frac{4}{9}\times 4$

$= \frac{16E}{9}$                ∴($E = \frac{k}{4}$)

So the energy of electron in 3rd orbit of He is $\frac{16E}{9}$ .