Question

An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct ?
(A) K.E, P. E. and T.E. decreases
(B) K.E. increases but P. E. and T.E. decreases
(C) K.E. and T.E. decreases but P.E. increases
(D) K.E. decreases, P.E. increases but T.E. remains the same

• A. A
• B. B
• C. C
• D. D

Hint:

In a Bohr orbit KE is the negative of total energy and PE is twice the total energy.

Answer 1

The Correct Option is B

Step 1: Energies in an orbit
\(K = -E_n\), \(U = 2E_n\), \(E_n = -\frac{13.6Z^2}{n^2}\ \text{eV}\).

Step 2: Transition to the ground state
The electron goes to a lower orbit, so \(E_n\) becomes more negative: total energy decreases.

Step 3: Effect on KE and PE
\(K = -E_n\) increases. \(U = 2E_n\) becomes more negative, so PE decreases.

Step 4: Result
KE increases while PE and TE decrease. Statement (B). Statement (A) is wrong since KE rises.

Final Answer:
KE increases while PE and TE decrease. \[ \boxed{\text{(B)}\ \text{KE increases, PE and TE decrease}} \]