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Energy of an electron is given by $E = - (2 .178 \times 10^{- 18} J) (Z^{2} / n^{2})$ . Wave length of light required to excite an electron in an hydrogen atom from level $n = 1$ to $n = 2$ will be: $(h = 6 .62 \times 10^{- 34} Js$ and $c = 3 .0 \times 10^{8} {ms}^{- 1})$

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$1.216 \times 10^{- 7} m$

$2.816 \times 10^{- 7} m$

$6.500 \times 10^{- 7} m$

$8.500 \times 10^{- 7} m$

answer is A.

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Detailed Solution

$ΔE = E_{2} - E_{1} ΔE = (- 2 .178 \times 10^{- 18} J) (\frac{1}{4} - \frac{1}{1}) ΔE = 1 .6335 \times 10^{- 18} J$

Thus, the wavelength,

$λ = \frac{hc}{ΔE} λ = \frac{(6 .62 \times 10^{- 34} J) (3 \times 10^{8} {ms}^{- 1})}{(1 .6335 \times 10^{- 18} J)} λ = 1 .216 \times 10^{- 7} m$

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