Given the value of Rydberg constant is 107 m-1, the wave number of the last line of the Balmer series in hydrogen spectrum will be [NEET 2016]

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Given the value of Rydberg constant is 10⁷ m^-1, the wave number of the last line of the Balmer series in hydrogen spectrum will be [NEET 2016]

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0.025 X 10⁴ m^-1

0.5 X 10⁷ m^-1

2.5 X 10⁷ m^-1

0.25 x 10⁷ m^-1

answer is B.

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Detailed Solution

Given, Rydberg constant, $R = 10^{7} m^{- 1}$

For last line in Balmer series, $n_{2} = \infty, n_{1} = 2$

As we know that,

$\frac{1}{λ} = R (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

$\Rightarrow \frac{1}{λ} = 10^{7} (\frac{1}{2^{2}} - \frac{1}{\infty})$

$v = \frac{1}{λ} = \frac{10^{7}}{4} = 0.25 \times 10^{7} m^{- 1}$

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