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Energy of an electron is given by $E = - 2.178 \times 10^{- 18} \times \frac{Z^{2}}{n^{2}}$ . Wavelength of light required to excite an electron in the hydrogen atom from level n= 1 to n= 2 will be

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

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

$1.214 \times 10^{- 7} m$

answer is D.

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Detailed Solution

$E = \frac{h c}{λ} = 2.178 \times 10^{- 18} Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$\frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{λ} = 2.178 \times 10^{- 18} \times {(1)}^{2} \times [\frac{1}{{(1)}^{2}} - \frac{1}{{(2)}^{2}}]$

$λ = 1.214 \times 10^{- 7} m$

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