Determination of Rydberg constant by studying Hydrogen spectrum

Objective:

To determination of Rydberg constant by studying Hydrogen spectrum.

Theory:

Balmer series is the emission spectrum associated with the transition of electrons from states with the principal quantum number n>2 to the state with n = 2. The wavelengths of the corresponding lines are expressed by a formula

1λ= RH (1n12- 1n22)

where, n1 = 2 and n2 > 2.

In Hydrogen spectrum there are a few bright lines, namely

Hα : n2 = 3 : Colour = Red

Hβ : n2 = 4 : Colour = Blue-green

Hγ : n2 = 5 : Colour = Violet

Hδ : n2 = 6 : Colour = Violet

In the present experiment wavelengths of these lines are determined by measuring the angle of diffraction by a transmission grating using the formula

a+bsinθ=nλ

Here α is the width of the opaque line in the grating and b is the width of the transparent region between two opaque lines and consequently a+b= 1N , where N is the number of rulings per unit length of the grating, n is the order of the spectrum and θ is the angle of diffraction.

Apparatus:

Spectrometer, Spirit level, Hydrogen discharge tube, Power supply for the discharge  tube. (A magnifying lens and a torch in hand may prove useful)

Experimental results:

  • Vernier Constant of the Spectrometer:
  •  Measurement of angle of Diffraction:

No. of Rulings N = ………………. per mm.=……………… per cm.

Calculation:

λred =

λblue-green =

λviolet-1 =

λviolet-2 =

RH from red line =

RH from blue-green line =

RH from violet-1 line =

RH from violet-2 line =

Average RH =

Standard value of RH =

Percentage Error:

Conclusion:

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