Quantization of orbital angular momentum in the Bohr model In early quantum theory (Bohr’s atomic model), the orbital angular momentum L of an electron is quantized in integral multiples of Planck’s constant divided by 2π. What is the smallest allowed (ground-state) orbital angular momentum in terms of Planck’s constant h?

Introduction / Context:
The Bohr model postulates that electrons revolve in stationary circular orbits around the nucleus with quantized angular momentum. Although superseded by modern quantum mechanics, this idea leads to correct spectral predictions for hydrogen and is a standard starting point for understanding angular momentum quantization.

Given Data / Assumptions:

• Bohr postulate: angular momentum is quantized.
• Planck’s constant is h, and ħ = h / (2π).
• Ground state corresponds to principal quantum number n = 1.

Concept / Approach:

Bohr’s hypothesis states L = n * h / (2π) = n * ħ, where n is a positive integer. The smallest allowed angular momentum occurs for n = 1 and equals ħ = h / (2π). This discrete set of values explains line spectra via transitions between allowed orbits.

Step-by-Step Solution:

Verification / Alternative check:

Modern quantum mechanics yields the same magnitude for the orbital angular momentum eigenvalues through ħ and quantum numbers, showing Bohr’s value aligns with ħ for n = 1 in the simple picture.

Why Other Options Are Wrong:

Values like h, 2πh, h/π, or h/4π do not match Bohr’s postulate for the ground state. Only h/(2π) equals ħ and is correct.

Common Pitfalls:

Confusing h with ħ, or forgetting the factor 2π that converts between them.

Final Answer:

h / (2π)