Question

The total energy of in the electron in the hydrogen atom in the ground state is $-13.6eV$. Which of the following is its kinetic energy in the first exited state?

• A. $13.6eV$
• B. $6.8eV$
• C. $3.4eV$
• D. $1.825eV$

Answer 1

Answer: (C)

$3.4eV$

Energy nth orbit of hydrogen atom is given by,

$E_n=\frac{-13.6}{n^2}e.V$

For ground state, $n=1$

$\therefore E_l=\frac{-13.6}{l^2}=-13.6eV$

for first excited state, $n=2$

$\therefore E_2=\frac{-136.6}{2^2}=\frac{-136.6}{4}=-3.4eV$

Kinetic energy of an electron in the first excited state is,

$K.E=-E_2$

$\Rightarrow K.E=3.4eV$