Question

In Bohr’s atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:

• A. All K, P and E increase
• B. K decreases, P and E increase
• C. P decreases, K and E increase
• D. K increases, P and E decrease

Answer 1

The Correct Option is B

To solve this question, we need to understand Bohr's atomic model, specifically the energy characteristics of an electron in a hydrogen atom. In Bohr's model, electrons orbit the nucleus in specific fixed orbits or energy levels.

In Bohr's model:

1. The n-th orbit (energy level) has a specific energy:
   E_n = -\frac{13.6}{n^2} \text{ eV}
2. Kinetic energy (K) in an orbit is positive and given by:
   K = \frac{13.6}{2n^2} \text{ eV}
3. Potential energy (P) in an orbit is negative and is:
   P = -\frac{13.6}{n^2} \text{ eV}
4. Total energy (E) is the sum of kinetic and potential energy:
   E = K + P = -\frac{13.6}{n^2} \text{ eV}

When an electron transitions to a higher energy level:

1. The value of n increases.
2. Kinetic energy (\(K\)) decreases because \frac{1}{n^2} is smaller for larger n:
   K = \frac{13.6}{2n^2} \text{ eV}\text{ decreases as }n\text{ increases}
3. Potential energy (\(P\)) becomes less negative, hence it increases (magnitude decreases):
   P = -\frac{13.6}{n^2} \text{ eV}\text{ becomes less negative/increases as }n\text{ increases}
4. Total energy (\(E\)) increases as it becomes less negative:
   E = -\frac{13.6}{n^2} \text{ eV}\text{ also becomes less negative/increases as }n\text{ increases}

Thus, the correct option when an electron undergoes transitions to a higher level is:

• Kinetic energy (K) decreases.
• Potential energy (P) increases.
• Total energy (E) increases.

The correct answer is "K decreases, P and E increase."