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The Balmer series is telling us the wavelength of the emitted wave when a transition from an upper level in the atom (bigger than 2) is made towards the level 2 of energy. Thus the value of m that we use in the Balmer-Ridberg equation to determine the wavelength of a certain transition is m=2. 
(For Lyman m=1, for Balmer m=2, for Paschen m=3, etc)

The value of  [tex]m[/tex] for the Balmer series in the Balmer-Rydberg equation is [tex]\boxed{m=2}[/tex] .

Further Explanation:

The Rydberg’s Equation is the equation that gives the mathematical relationship between the different spectral lines. This relation states that the wavenumber of the successive spectral lines are integral multiples of one another.

The expression for the Rydberg’s formula is given as:

[tex]\boxed{\frac{1}{\lambda }=R{Z^2}\left({\frac{1}{{{m^2}}}-\frac{1}{{{n^2}}}}\right)}[/tex]

Here, [tex]\lambda[/tex]  is the wavelength of the photon, [tex]R[/tex]  is the Rydberg’s constant, [tex]Z[/tex]  is the atomic number of the element and [tex]m\,\&\,n[/tex]  are the integers representing various spectral lines.

The spectrum of a hydrogen atom consists of the five different spectral lines. These spectral lines are named as:

  • Lyman series [tex]\left({m = 1}\right)[/tex] .
  • Balmer series [tex]\left({m=2}\right)[/tex] .
  • Paschen series [tex]\left({m=3}\right)[/tex] .
  • Bracket series [tex]\left({m=4}\right)[/tex] .
  • Pfund series [tex]\left({m=5}\right)[/tex] .

The variable [tex]m[/tex]  in the Rydberg’s formula represent the start of the spectral line and the variable [tex]n[/tex]  represents the end of the spectrum.

If the emission starts from the Balmer series and then goes further ahead to the different spectral lines, the value of [tex]m[/tex]  will be [tex]2[/tex]  and the value of [tex]n[/tex]  will vary from [tex]2\to\infty[/tex] .

Therefore, the value of [tex]m[/tex]  in the Rydberg’s formula for the Balmer series is [tex]\boxed{m=2}[/tex] .

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Answer Details:

Grade: High school

Subject: Physics

Chapter: Hydrogen Spectrum

Keywords:

Lyman, Balmer, series, Rydberg, constant, wavelength, hydrogen spectrum, spectral line, m=2, Rydberg-Balmer equation,

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