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If the radius of the first Bohr orbit of a hydrogen atom is a₀, what is the de Broglie wavelength of the electron in the third orbit?
- 4πa₀
- 8πa₀
- 6πa₀
- 2πa₀
Correct answer: 6πa₀
Solution
The de Broglie wavelength of an electron in a Bohr orbit is determined by the orbit's radius and the quantization condition, which states that the circumference of the orbit must be an integer multiple of the wavelength. For the third orbit, the radius is 3 times the first orbit's radius (3a₀), leading to a wavelength of 6πa₀ when applying the de Broglie relation.
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