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QPages 384-386: Q45: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q45 Solution: Suppose in an imaginary world the angular momentum is quantized …

Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2πh/2\pi. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?

Step-by-Step Verified Solution

**Answer:** Longest wavelength = 656 nm (H_ line). **Step-by-Step Explanation:** If angular momentum is quantized to even multiples of h/2�, then mvr = 2n_. This changes the energy levels: E_n = _13.6/(4n_) eV. The longest wavelength in visible range would be the transition from n=2 to n=1 of this modified system. E = 13.6/4 (1/1_ _ 1/2_) = 13.6/4 _ 3/4 = 2.55 eV. _ = 1240/2.55 = 486 nm. Standard: 656 nm [citation:3].

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