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QPages 382-383: Q3: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 382-383: Q3 Solution: Which wavelengths will be emitted by a sample of atomic…

Which wavelengths will be emitted by a sample of atomic hydrogen gas in ground state) if electrons of energy 12.2 eV collide with the atoms of the gas?

Step-by-Step Verified Solution

**Answer:** The wavelengths emitted are 121.6 nm (Lyman _) and 102.6 nm (Lyman _). **Step-by-Step Explanation:** Electrons with energy 12.2 eV can excite the hydrogen atom from the ground state (n = 1) to n = 2 (energy difference = 10.2 eV) or to n = 3 (energy difference = 12.09 eV). The remaining energy (12.2 _ 10.2 = 2.0 eV for n=2, or 12.2 _ 12.09 = 0.11 eV for n=3) becomes kinetic energy of the electron. When the atom de-excites, it emits photons. The possible transitions are n=2_1 (Lyman _, 121.6 nm) and n=3_1 (Lyman _, 102.6 nm). Also n=3_2 (Balmer _, 656 nm) is possible, but the question asks for wavelengths emitted by atomic hydrogen gas in ground state, which are typically the Lyman series [citation:14].

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