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Question: Energy of the electron in n<sup>th</sup> orbit of hydrogen atom is given by \(E_{n} = - \frac{13.6}{...

Energy of the electron in nth orbit of hydrogen atom is given by En=−13.6n2eVE_{n} = - \frac{13.6}{n^{2}}eV. The amount of energy needed to transfer electron from first orbit to third orbit is.

A

13.6 eV

B

3.4 eV

C

12.09 eV

D

1.51 eV

Answer

12.09 eV

Explanation

Solution

For n=1, 6muE1=−13.6(1)2=−13.6 6mueVn = 1,\mspace{6mu} E_{1} = - \frac{13.6}{(1)^{2}} = - 13.6\mspace{6mu} eV

and for n = 3, E3=−13.6(3)2=−1.51 6mueVE_{3} = - \frac{13.6}{(3)^{2}} = - 1.51\mspace{6mu} eV

So required energy

=E3−E1=−1.51−(−13.6)=12.09 6mueV= E_{3} - E_{1} = - 1.51 - ( - 13.6) = 12.09\mspace{6mu} eV