Modern Physics Lab(381) 2016
1 H.A.B
Balmer series of hydrogen
Objective of the experiment
- Observing the spectral line of hydrogen with high resolution grating.
- Measuring the wavelengths H(red), H(green) and H(blue) from Balmer series.
- Determining the Rydberg constant R.
Theory
When the light from such a low-pressure gas discharge is examined with spectroscope, it is found to consist of a few bright lines of pure color on a generally dark background.
The wavelengths contained in a given line spectrum are characteristic of the particular element emitting the light. Since no two elements emit the same line spectrum, this phenomenon represents a sensitive technique for identifying the elements present in unknown sample.
Balmer (1825-1898) found a formula that correctly predicted the wavelengths of visible emission lines of hydrogen: H(red), H(green), H(blue) and H (violet).
Following figure shows these lines in the emission spectrum of hydrogen. The four visible line occur at the wavelengths
656.3nm, 486.1nm, 434.1nm and 410.2nm. the wavelengths of theses lines called (the Balmer series) can be described by the empirical equation:
2 12
2 1 1
R n
.
Where R is a constant called Rydgerg constant, R=1.097 x 107 m-1.
The H(red) line in Balmer series at
656.3nm corresponding to n=3 in equation. The H(green) line in at 486.1nm corresponding to n=4, and so on.
Later the Balmer formula was explained in the framework of the Bhor atom model (following fig.).
In the experiment, the emission spectrum is excited by means of a Balmer lamp which is filled with water vapour. The water molecules are decomposed by electric discharge into excited atomic hydrogen and a hydroxyl group. The wavelengths H(red), H(green) and H(blue) are determined with a high-resolution grating. In the first order of the grating, the relation between the wavelength and the angle of observation is
) sin(
d
Modern Physics Lab(381) 2016
2 H.A.B
d: grating constant.
The measured values compared with wavelengths calculated according to the Balmer formula.
From the figure,
2
) 2
sin(
b a
b
b b d a
2 2
Where b is the distance between the lines and the zeroth order on the screen and a is the distance between the Rowland grating and the translucent screen.
Distance of the grating a (see Fig.) a = a1 + a2+ d1/2 + d2.
Apparatus Balmer lamp.
power supply unit for Balmer lamps.
copy of a Rowland grating.
lens, f = + 50 mm.
lens, f = + 100 mm.
adjustable slit.
translucent screen.
steel tape measure, 2 m.
Setup Remark:
The spectral lines can only be observed in a completely darkened room.
The experimental setup is illustrated in the opposite Figure.
Experimental setup for studying the Balmer series of atomic hydrogen (the figures indicate the positions of the left edges of the multi clamps on the optical bench).
a Balmer lamp
b imaging lens f = 50 mm c adjustable slit
d imaging lens f = 100 mm e grating
f screen
Modern Physics Lab(381) 2016
3 H.A.B
– Move the copy of a Rowland grating into the ray path.
– Darken the experiment room completely, and observe the translucent screen in transmission.
– Narrow the adjustable slit until separate lines are visible on the screen.
– If necessary, block unwanted light from the Balmer lamp with a masking plate made from cardboard.
– Mark the positions of the lines and of the zeroth order on the screen.
– Measure the distances b between the lines and the zeroth order on the screen.
– Determine the distance a between the Rowland grating and the translucent screen.
-calculate wavelengths of the lines H(red), H(green) and H(blue) and plot it as a function of the term
2 12 2
1 n
The slope of the straight line through the origin drawn in the graph is R.
