Line Spectra (Rydberg’s Constant)

Experiment 9

Younes Sina

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.

Objective

Theoryexcited state

When an element is heated strongly

when a gas at low pressure is subjected to a high electric potential

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

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

Planck's law

In the case of hydrogen, the transitions that can occur are shown in the diagram below:     

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.

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

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.

Calculations

λ62 = ? nm, λ52 = ? nm, λ42 = ? nm, λ32 = ? nm,

Raccepted = 1.097x107m-1