Question

a) Calculate the energy values of the electron in the second orbit of hydrogen
atom. What will be the radius of this orbit?

Answer 1

Answer: The energy of an electron in the second orbit of hydrogen  atom is $5.4475\times 10^{-22} J$.

The radius of the second orbit :$2.1168\times 10^{-10} m$

Explanation:

The energy on the nth orbital is given by = $E_n=k\frac{Z^2}{n^2}$

Where  k= $2.179\times 10^{-18} J$

The energy of an electron in the second orbit of hydrogen  atom :

n = 2, Z=1

$E_n=2.179\times 10^{-18} J\frac{(1)^2}{(2)^2}=5.4475\times 10^{-22} J$

The radius of the nth orbit is given by ;$r_n=\frac{n^2}{Z}\times a_o$

$a_o=5.292\times 10^{-11} m$

The radius of the second orbit :

$r_2=\frac{(2)^2}{1}\times 5.292\times 10^{-11} m=2.1168\times 10^{-10} m$