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Question: The wave number of the \({{H}_{\alpha }}\) – line in balmer series of hydrogen spectrum is: A. 5R/...

The wave number of the Hα{{H}_{\alpha }} – line in balmer series of hydrogen spectrum is:
A. 5R/36
B. 3R
C. 21R/100
D. 3R/4

Explanation

Solution

Balmer series is going to form in a hydrogen spectrum when an electron does transitions from third energy level to second energy level.
We can calculate the wave number of Hα{{H}_{\alpha }} – line in the balmer series of the hydrogen spectrum by using the following formula.
v− =R[1n12−1n22]\overset{-}{\mathop{v}}\,=R\left[ \dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}} \right]
v− \overset{-}{\mathop{v}}\, = Wave number
R = Rydberg constant
n1{{n}_{1}} = lower energy level
n2{{n}_{2}} = higher energy level

Complete step-by-step answer: - In the question it is given that to find the wave number of the Hα{{H}_{\alpha }} – line in the balmer series of hydrogen spectrum.
- We know that Hα{{H}_{\alpha }} – line in the balmer series of the hydrogen spectrum is going to form when an electron does transitions from third energy level to second level.
- So, by using the following formula we can calculate the wavenumber corresponding to balmer series.
v− =R[1n12−1n22]\overset{-}{\mathop{v}}\,=R\left[ \dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}} \right]
v− \overset{-}{\mathop{v}}\, = Wave number
R = Rydberg constant
n1{{n}_{1}} = lower energy level in Hα{{H}_{\alpha }} – line in balmer series of hydrogen spectrum = 2
n2{{n}_{2}} = higher energy level in Hα{{H}_{\alpha }} – line in balmer series of hydrogen spectrum = 3

& \overset{-}{\mathop{v}}\,=R\left[ \dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}} \right] \\\ & \overset{-}{\mathop{v}}\,=R\left[ \dfrac{1}{{{2}^{2}}}-\dfrac{1}{{{3}^{2}}} \right] \\\ & \overset{-}{\mathop{v}}\,=\dfrac{5R}{36} \\\ \end{aligned}$$ \- Therefore the wave number of the ${{H}_{\alpha }}$ – line in the balmer series of the hydrogen spectrum is 5R/36. **So, the correct option is A.** **Note:** Wavenumber is the reciprocal of the wavelength and wavelength is going to be denoted with a symbol $\lambda $ and wave number is going to be denoted with $\overset{-}{\mathop{v}}\,$. ${{H}_{\alpha }}$ – line in the balmer series of hydrogen spectrum appears in deep-red visible color in the hydrogen spectrum.