The document describes an experiment to measure Rydberg's constant using the emission spectrum of hydrogen. Electrons in hydrogen atoms absorb energy and transition to higher energy levels. When they drop down, they emit photons of specific wavelengths according to Planck's law. By measuring the wavelengths of photons emitted during transitions from higher to lower energy levels in the Balmer series, Rydberg's constant can be calculated and verified. Measurements of hydrogen's spectral lines will be used to calculate Rydberg's constant and compare to the accepted value.

1. Experiment 9
Line Spectra
(Rydberg’s Constant)
Younes Sina

2. Objective
 Use the emission spectrum of hydrogen atom in
order to verify the relation between energy
levels and the photon wavelength
 Calculate Rydberg’s constant R = 1.097x107m-1.

3. Theory
excited state
 When an element is heated strongly
 when a gas at low pressure is subjected to a high electric potential

4. When an element is heated strongly, or when a gas at low
pressure is subjected to a high electric potential, the element
begins to glow, indicating that it is emitting energy in the
visible region of the spectrum. This arises from electrons that
have absorbed a certain amount of energy and have been
promoted to a higher energy state. When the electrons revert
to a lower energy state, they lose energy by emitting
photons whose energy corresponds to the energy loss, E.
E = hc/λ

5. Planck's law
E = hc/λ
h : Planck's constant (6.63x10-34 J.s-1)
c : velocity of light in a vacuum (3.00x108 m.s-1)
λ: wavelength of the emitted photon
In the case of hydrogen, the transitions that can occur are shown in the
diagram below:

6. Only the transitions down to n = 2 have energy values such
that the associated wavelengths occur in the visible region
of the spectrum. These give rise to the so-called Balmer
series of lines, known as an ATOMIC EMISSION SPECTRUM.
The other series occur either in the infrared region
(Lyman), or in the ultraviolet region (Paschen, Brackett,
Pfund). These series are named after their discoverers.

15. Goal
Reading absorption spectrum of hydrogen atom using cold hydrogen tube
Reading wavelengths at which the dark lines appear
Reading spectral emission lines in the spectroscope using hot hydrogen tube
Observing spectral emission lines in the spectroscope using hot helium tube

16. Calculations
 Use the Balmer Series equation to calculate R for each of the
measured wavelengths. Next, find the average value of R. It
gives the measured value for R.
 Calculate a %error on R using the usual %error formula.
λ62 = ? nm, λ52 = ? nm, λ42 = ? nm, λ32 = ? nm,
Raccepted = 1.097x107m-1