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An electron in a higher energy level of a Li²⁺ ion possesses an angular momentum of 3h/2π. The electron's de Broglie wavelength in this energy state is expressed as pπa₀ (where a₀ represents the Bohr radius). Determine the value of p.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

The angular momentum quantization condition for a hydrogen-like atom is L = nh/2π. Given L = 3h/2π, the principal quantum number n = 3. The de Broglie wavelength is inversely proportional to the momentum, and for n = 3, the wavelength is 2πa₀, making p = 2.

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