Question

Assertion : In Bohr model of hydrogen atom, the angular momentum of an electron in \( n \)th orbit is proportional to the square root of its orbit radius \( r_n \)

Reason (R): According to Bohr model, electron can jump to its nearest orbits only.

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

Hint:

In the Bohr model, the electron's angular momentum is quantized and proportional to the radius of the orbit.

Answer 1

The Correct Option is C

We are given an assertion (A) and a reason (R) related to Bohr's model of the hydrogen atom. Let's analyze both statements:

1. Assertion (A): "In Bohr's model of the hydrogen atom, the angular momentum of an electron in the \(n\)-th orbit is proportional to the square root of its orbit radius \(r_n\)."

This statement is incorrect. According to Bohr's model, the angular momentum (\(L\)) of an electron in the \(n\)-th orbit is quantized and is given by the equation:

\[ L = n \hbar \]

where:

• \(L\) is the angular momentum of the electron,
• \(n\) is the principal quantum number (the orbit number), and
• \(\hbar\) is the reduced Planck’s constant.

The radius \(r_n\) of the \(n\)-th orbit is proportional to \(n^2\), i.e.,

\[ r_n \propto n^2 \]

Therefore, the angular momentum is proportional to the quantum number \(n\), not to the square root of the radius. The assertion is therefore incorrect.

2. Reason (R): "According to Bohr's model, the electron can jump to its nearest orbits only."

This statement is correct. In Bohr's model, when an electron absorbs or emits energy, it jumps from one orbit to another. However, the electron can only jump between specific orbits that correspond to the allowed energy levels. These energy levels are quantized, and the electron can only transition between these discrete orbits (energy levels) in response to energy absorption or emission. This transition typically occurs between orbits that are closest to each other in energy. Therefore, the reason is true.

3. Evaluation of the Assertion and Reason:

While the reason (R) is correct, the assertion (A) is incorrect because, according to Bohr’s model, the angular momentum is proportional to \(n\), not the square root of the radius. Therefore, the assertion is false, even though the reason is true.

4. Conclusion:

The correct answer is: Assertion is false, and Reason is true.