Question

Given below are two statements: one is labeled as Assertion (A) and the other is labeled as Reason (R).
Statement-1: According to Bohr’s Model, angular momentum is Quantized for stationary orbits.
Statement-2: Bohr’s Model doesn’t follow Heisenberg’s Uncertainty Principle.
In the light of the above statements, write the detailed answer:

• A. Both Statement - 1 and statement - 2 are true
• B. Statement - 1 is true and statement - 2 is false
• C. Statement - 1 is false and statement - 2 is true
• D. Both Statement - 1 and statement - 2 are false

Hint:

Bohr’s model is a stepping stone to modern quantum mechanics but does not align with the uncertainty principle.

Answer 1

The Correct Option is A

To solve this question, we need to analyze both Statement-1 and Statement-2 concerning the Bohr model of the atom and its compliance with various principles in physics.

1. Examine Statement-1: "According to Bohr’s Model, angular momentum is quantized for stationary orbits."
   • In Bohr's model of the hydrogen atom, the electron moves in certain specific circular orbits around the nucleus without radiating energy.
   • The angular momentum of the electron in these stationary orbits is quantized, given by the formula: L = n \hbar, where n is the principal quantum number and \hbar is the reduced Planck's constant \left(\hbar = \frac{h}{2\pi}\right).
   • This quantization condition is a fundamental postulate of the Bohr model, which successfully explains the spectral lines of hydrogen.
   • Therefore, Statement-1 is true.
2. Examine Statement-2: "Bohr’s Model doesn’t follow Heisenberg’s Uncertainty Principle."
   • Heisenberg's Uncertainty Principle states that there is an inherent limit to the precision with which complementary variables such as position and momentum can be known simultaneously.
   • The Bohr model assumes definite orbits for electrons, implying precise knowledge of both position and momentum, which conflicts with Heisenberg's principle.
   • Therefore, the Bohr model is inconsistent with the uncertainty principle, meaning Statement-2 is true.

Conclusion: Both Statement-1 and Statement-2 are true. The Bohr model, while an important historical step in atomic theory, is limited by its non-compliance with quantum mechanical principles like the Heisenberg Uncertainty Principle.