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Hydrogen (¹H¹), Deuterium (¹H²), singly ionised Helium (²He⁴⁺) and doubly ionised lithium (³Li⁶⁺) all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wavelengths of emitted radiation are λ1, λ2, λ3 and λ4 respectively then approximately which one of the following is correct ?

1. λ1 = 2λ2 = 2λ3 = λ4
2. λ1 = λ2 = 4λ3 = 9λ4
3. λ1 = 2λ2 = 3λ3 = 4λ4
4. 4λ1 = 2λ2 = 2λ3 = λ4

Correct answer: λ1 = λ2 = 4λ3 = 9λ4

Solution

The wavelengths of emitted radiation during electron transitions are inversely proportional to the energy levels of the electrons in the atoms. Since the energy levels depend on the atomic number and the electron configuration, the ratios of the wavelengths can be derived from the differences in these energy levels for each atom. In this case, the correct option reflects the relationship between the wavelengths based on the respective atomic structures and their transitions.

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