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Chemistry Question on Bohr’s Model for Hydrogen Atom

Which is the shortest wavelength line in the Lyman series of the hydrogen spectrum? (R=1.097×10−2nm−1)\left(R=1.097 \times 10^{-2} nm ^{-1}\right)

A

94.21 nm

B

91.16 nm

C

911.6 nm

D

933.6 nm

Answer

91.16 nm

Explanation

Solution

For Lyman series, 1λ=R(1(1)2−1n2)\frac{1}{\lambda}=R\left(\frac{1}{(1)^{2}}-\frac{1}{n^{2}}\right)
hence, for λ\lambda to be smallest, nn should be greatest (i.e.,∞\infty)
∴1λmin⁡=1.097×10−2(1−1∞2)\therefore \frac{1}{\lambda_{\min }} =1.097 \times 10^{-2}\left(1-\frac{1}{\infty^{2}}\right)
=1.097×10−2=1.097 \times 10^{-2}
or λmin⁡=11.097×10−2=91.16 nm\lambda_{\min }=\frac{1}{1.097 \times 10^{-2}}=91.16\, nm