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Energy of an electron is given by E = -2.178 × 10⁻¹⁸ J (Z²/n²). Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be: (h = 6.62 × 10⁻³⁴ Js and c = 3.0 × 10⁸ m s⁻¹)

1. 6.500 × 10⁻⁷ m
2. 8.500 × 10⁻⁷ m
3. 1.214 × 10⁻⁷ m
4. 2.816 × 10⁻⁷ m

Correct answer: 1.214 × 10⁻⁷ m

Solution

The energy difference between the two levels (n=1 and n=2) in a hydrogen atom can be calculated using the formula provided, and then the wavelength can be determined using the relationship between energy and wavelength (E = hc/λ). The correct option corresponds to the wavelength that matches the calculated energy difference for the transition.

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