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Calculate the maximum wavelength of Balmer series in the hydrogen spectrum. Calculate the corresponding wavenumber.
R=1.097×107m1

Answer
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Hint: In this solution, we are going to use Rydberg's formula to calculate the wavelength of Balmer series. The maximum wavelength in the Balmer series is obtained corresponding to minimum energy transition, that is, when electron transition occurs between 2nd and 3rd shell.

Formula Used:
Rydberg’s Formula:
1λ=R×Z2(1n121n22)m1
Where,
Ris Rydberg’s Constant
Z is the Atomic Number
n1 is lower energy state
n2 is higher energy state
λ is Wavelength corresponding to electron’s transition between shells n1and n2

Complete step by step answer:
Given:
Z=1 (As atomic number of Hydrogen is 1)
R=1.097×107m1
n1=2 (As ground state of Balmer series is 2)
Now, for the maximum wavelength to be emitted, the transition of the electron should take place in such a way that the corresponding energy released should be minimum.
And, for minimum energy, the transition of electrons should take place between two closest energy states.
As we know that, For Balmer series, the ground state n1=2 so, for minimum energy, the closest energy state would be the just next energy state, that is, n2=3
Substituting the values of R,Z,n1andn2in Rydberg’s Formula, we get,
1λ=(1.097×107m1)×(1)2(1(2)21(3)2)1λ=1.097×107×1(1419)m11λ=1.097×107(536)m11λ=1.524×106m1
λ=0.656×106m λ=656×109m λ=656nm 
Therefore, the maximum wavelength of the Balmer series in the hydrogen spectrum is 656nm.
And, the wave number is given by 1λ . So, the wave number corresponding to maximum wavelength of Balmer series in the hydrogen spectrum is given by:
Wave number 1λ=1.524×106m1

Additional information:
The maximum wavelength of Balmer series in the hydrogen spectrum corresponds to a transition between 2nd and 3rd shell, similarly for minimum wavelength of Balmer series in the hydrogen spectrum will corresponds to a transition between 2nd shell and .

Note:
While applying Rydberg's Formula, always remember that n2 is a higher shell while n1 is a lower shell. If both interchanged wave numbers or wavelengths will come out to be negative which is not possible.
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