Question

When the hydrogen atom is excited from the ground state,

• A. potential energy increases but kinetic energy decreases
• B. both potential energy and kinetic energy decrease
• C. both potential energy and kinetic energy increase
• D. potential energy decreases but kinetic energy increases
• E. there is no change in the total energy

Hint:

Remember that in the context of quantum mechanics, increased potential energy for an electron means it is less bound to the nucleus, contrary to classical interpretations.

Answer 1

The Correct Option is A

Step 1: In quantum mechanics, the total energy of a hydrogen atom is given by the negative of its potential energy divided by two, \( E = -\frac{PE}{2} \). 
Step 2: When an atom is excited, the electron moves to a higher energy level, which means it is further from the nucleus. 
Step 3: This increases the potential energy (less negative) because the electron is less tightly bound to the nucleus. 
Step 4: Simultaneously, according to the virial theorem for the hydrogen atom, the kinetic energy \( KE \) is \(-\frac{PE}{2}\), thus decreasing in magnitude as the potential energy becomes less negative. 
Step 5: Therefore, upon excitation, the potential energy increases (becomes less negative) and the kinetic energy decreases.