
Calculate the maximum wavelength of Balmer series in the hydrogen spectrum. Calculate the corresponding wavenumber.
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 and shell.
Formula Used:
Rydberg’s Formula:
Where,
is Rydberg’s Constant
is the Atomic Number
is lower energy state
is higher energy state
is Wavelength corresponding to electron’s transition between shells and
Complete step by step answer:
Given:
(As atomic number of Hydrogen is 1)
(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 so, for minimum energy, the closest energy state would be the just next energy state, that is,
Substituting the values of in Rydberg’s Formula, we get,
Therefore, the maximum wavelength of the Balmer series in the hydrogen spectrum is .
And, the wave number is given by . So, the wave number corresponding to maximum wavelength of Balmer series in the hydrogen spectrum is given by:
Wave number
Additional information:
The maximum wavelength of Balmer series in the hydrogen spectrum corresponds to a transition between and shell, similarly for minimum wavelength of Balmer series in the hydrogen spectrum will corresponds to a transition between shell and .
Note:
While applying Rydberg's Formula, always remember that is a higher shell while is a lower shell. If both interchanged wave numbers or wavelengths will come out to be negative which is not possible.
Formula Used:
Rydberg’s Formula:
Where,
Complete step by step answer:
Given:
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
Substituting the values of
Therefore, the maximum wavelength of the Balmer series in the hydrogen spectrum is
And, the wave number is given by
Wave number
Additional information:
The maximum wavelength of Balmer series in the hydrogen spectrum corresponds to a transition between
Note:
While applying Rydberg's Formula, always remember that
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