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Question:

Energy of an electron is given by E = -2.178 × 10⁻¹⁸ J Z²/n². Wavelength of light required to excite an electron in a hydrogen atom from level n=1 to n=2 will be: [h = 6.62 × 10⁻³⁴ Js and c = 3.0 × 10⁸ ms⁻¹] 1.214 × 10⁻⁷m, 2.816 × 10⁻⁷m, 6.500 × 10⁻⁷m, 8.500 × 10⁻⁷m

6.500 × 10⁻⁷m

8.500 × 10⁻⁷m

2.816 × 10⁻⁷m

1.214 × 10⁻⁷m

Solution:

E₁ = hc/λ = 2.178 × 10⁻¹⁸ × z²[1/1² - 1/2²]
E₂ = hc/λ = 2.178 × 10⁻¹⁸ × z²[1/2² - 1/1²]
So, ΔE = E₂ - E₁
ΔE = hc/λ = 2.178 × 10⁻¹⁸ × z²[1/1² - 1/2²] → λ = 1.214 × 10⁻⁷m