Question

Assertion (A) : In Bohr model of hydrogen atom, the energy levels are discrete and quantised. Reason (R) : In a hydrogen atom, the electrostatic force on the electron provides the necessary centripetal force to it to revolve around the nucleus.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

In Bohr's model: \[ \text{Electrostatic force} \rightarrow \text{Centripetal force} \] but \[ \text{Quantised energy levels} \rightarrow mvr=\frac{nh}{2\pi}. \] Do not confuse these two independent conditions.

Answer 1

The Correct Option is B

Concept: Bohr proposed that electrons revolve around the nucleus only in certain permitted orbits for which the angular momentum is quantised: \[ mvr=\frac{nh}{2\pi}, \qquad n=1,2,3,\dots \] Because only certain orbits are allowed, the corresponding energies are also discrete and quantised. The electrostatic force between the electron and the nucleus indeed provides the centripetal force necessary for circular motion: \[ \frac{1}{4\pi\varepsilon_0}\frac{e^2}{r^2} = \frac{mv^2}{r}. \] However, this condition alone does not explain why only discrete energy levels exist.

Step 1: Examine the Assertion (A).
The energy of the electron in the \(n^{\text{th}}\) orbit is \[ E_n=-\frac{13.6}{n^2}\text{ eV}. \] Since \(n\) can take only integral values, the energy levels are discrete. Hence, Assertion (A) is true.

Step 2: Examine the Reason (R).
The electrostatic force indeed acts as the centripetal force: \[ \frac{1}{4\pi\varepsilon_0}\frac{e^2}{r^2} = \frac{mv^2}{r}. \] Therefore, Reason (R) is also true.

Step 3: Determine whether the reason explains the assertion.
The discreteness of energy levels arises due to the quantisation condition \[ mvr=\frac{nh}{2\pi} \] and not merely because the electrostatic force provides centripetal force. Therefore, the Reason is true but is not the correct explanation of the Assertion. Hence, \[ \boxed{\text{Both A and R are true, but R is not the correct explanation of A.}} \]