Given below are two statements: Statement I : According to Bohr's model of hydrogen atom, the angular momentum of an electron in a given stationary state is quantised. Statement II : The concept of electron in Bohr's orbit, violates the Heisenberg uncertainty principle. In the light of the above statements, choose the most appropriate answer from the options given below:

Both Statement I and Statement II are correct

Both Statement I and Statement II are incorrect

Statement I is correct but Statement II is incorrect

Statement I is incorrect but Statement II is correct

Structure of Atom PYQ — JEE Main 2023 · 15 Apr · Shift 1 · Q8 with Solution

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Correct answer: C

Analyze Statement I

According to Bohr’s model, the electron can move only in certain allowed circular orbits, called stationary states.

Bohr’s quantisation condition is: $mvr = \frac{nh}{2\pi} = n\hbar$ where $n = 1,2,3,\dots$

Since angular momentum is: $L = mvr$ it follows that: $L = n\hbar$

Therefore, the angular momentum of the electron is quantised in a stationary state.

So, Statement I is correct.
Analyze Statement II

In Bohr’s model, the electron is assumed to revolve in a definite circular orbit with fixed radius and fixed momentum.

That means both the position and momentum of the electron are being specified simultaneously with precision.

But Heisenberg’s uncertainty principle states: $\Delta x\, \Delta p \ge \frac{\hbar}{2}$

Hence, assigning a definite orbit to the electron is inconsistent with the uncertainty principle.

So, Statement II is also correct.
Evaluate the options
- A: Both incorrect — false
- B: Statement I correct, Statement II incorrect — false
- C: Both correct — true
- D: Statement I incorrect, Statement II correct — false
Final Answer

The correct option is: $\boxed{\text{C}}$

View written solutionFree

Correct answer: C

Analyze Statement I

According to Bohr’s model, the electron can move only in certain allowed circular orbits, called stationary states.

Bohr’s quantisation condition is: $mvr = \frac{nh}{2\pi} = n\hbar$ where $n = 1,2,3,\dots$

Since angular momentum is: $L = mvr$ it follows that: $L = n\hbar$

Therefore, the angular momentum of the electron is quantised in a stationary state.

So, Statement I is correct.
Analyze Statement II

In Bohr’s model, the electron is assumed to revolve in a definite circular orbit with fixed radius and fixed momentum.

That means both the position and momentum of the electron are being specified simultaneously with precision.

But Heisenberg’s uncertainty principle states: $\Delta x\, \Delta p \ge \frac{\hbar}{2}$

Hence, assigning a definite orbit to the electron is inconsistent with the uncertainty principle.

So, Statement II is also correct.
Evaluate the options
- A: Both incorrect — false
- B: Statement I correct, Statement II incorrect — false
- C: Both correct — true
- D: Statement I incorrect, Statement II correct — false
Final Answer

The correct option is: $\boxed{\text{C}}$