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MCQEasyJEE 2023Bohr's Model & Hydrogen Spectrum

JEE Physics 2023 Question with Solution

The angular momentum of an electron in Bohr's orbit is LL. If the electron is assumed to revolve in the second orbit of a hydrogen atom, the change in angular momentum will be:

  • A

    L1/2L^{1}/_{2}

  • B

    Zero

  • C

    LL

  • D

    2L2L

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: The angular momentum in the first Bohr orbit is LL.

Find: The change in angular momentum when the electron moves to the second orbit.

In Bohr's model, angular momentum is quantized as

Ln=nh2πL_n = \frac{nh}{2\pi}

where nn is the principal quantum number.

For the first orbit, n=1n = 1, so

L1=1⋅h2π=LL_1 = \frac{1 \cdot h}{2\pi} = L

For the second orbit, n=2n = 2, so

L2=2⋅h2π=2LL_2 = \frac{2 \cdot h}{2\pi} = 2L

Therefore, the change in angular momentum is

ΔL=L2−L1=2L−L=L\Delta L = L_2 - L_1 = 2L - L = L

Therefore, the change in angular momentum is LL. The correct option is C. The solution lists option A, but its worked steps conclude ΔL=L\Delta L = L, which matches option C.

Common mistakes

  • Using the second-orbit angular momentum 2L2L as the change. This is wrong because the question asks for the increase relative to the initial orbit. Subtract the initial angular momentum: ΔL=L2−L1\Delta L = L_2 - L_1.

  • Assuming angular momentum remains unchanged between Bohr orbits. This is wrong because Bohr angular momentum is quantized and depends on nn. Use Ln=nh2πL_n = \frac{nh}{2\pi} to compare the two orbits.

  • Trusting the solution's printed option label without checking the working. This is wrong because the displayed label and the derivation disagree here. Follow the equations, which give ΔL=L\Delta L = L, and then map that value to the correct option.

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