Target Exam

CUET

Subject

Physics

Chapter

Atoms

Question:

The kinetic energy of an electron in the H-atom in the second excited state is $k$ units. Its total energy and potential energy, respectively, in the ground state will be

Options:

$-9k,-18k$

$-k, 2k$

$-4k, 16k$

$-k,2k$

Correct Answer:

$-9k,-18k$

Explanation:

The correct answer is Option (1) → $-9k,-18k$

Energy of electron in hydrogen atom:

$E_n=-\frac{13.6}{n^2}\ \text{eV}$

Second excited state $\Rightarrow n=3$

Total energy: $E_3=-\frac{13.6}{9}=-\frac{13.6}{9}$

Kinetic energy: $K=-E_3=\frac{13.6}{9}=k$

Ground state $n=1$:

Total energy: $E_1=-13.6\ \text{eV}=-9k$

Potential energy: $U=2E=-27.2\ \text{eV}=-18k$