Question

In this problem we will investigate absorption saturation. A cell contains a mixture of sodium (Na) vapour and helium (He) gas. The cell is heated to a temperature of 630°K and reaches thermal equilibrium. The sodium density is Nₙₐ = 1.532 × 10²¹m⁻³ and the helium density is NHe = 6.52×10²⁵m⁻³ . A transition between the lowest energy level and an excited energy level in the sodium atoms has an excitation energy of ∆E = 2.1eV. The excited level has a radiative decay rate of 6.3×10⁷ sec⁻¹ . The collisions between the helium and sodium atoms induce a broadening of the transitions. The contribution of the collisions to the transition linewidth is given by

∆Vₒₗ = Nₕₑ / π σc [ 8ₖᵦT / π (1 / Mₕₑ + 1 / Mₙₐ)¹/² ,

where σc = 10⁻¹⁴ cm² is the collision cross section, MHe = 6.647 × 10⁻²⁷ kg is the mass of a helium atom, and MNa = 3.818×10⁻²⁶ kg is the mass of a sodium atom.

Calculate the natural (radiative) linewidth ∆Vₐ, the linewidth due to Doppler broadening ∆V, and the linewidth due to collisions ∆Vₒₗ.

Answer 1

The question concerns the broadening of spectral lines in atomic spectroscopy, encompassing natural, Doppler, and collisional broadening mechanisms.

Step-by-step explanation:

The student is asking about the different types of broadening mechanisms that affect the absorption and emission lines in atomic spectroscopy. When an atom transitions between energy levels, the spectral line corresponding to the transition can be broadened by a variety of factors, including the natural (radiative) decay of the excited state, Doppler broadening due to thermal movement of atoms, and collisional broadening from interactions with other atoms. The radiative or natural linewidth (∆V_a) relates to the uncertainty in energy due to the finite lifetime of the excited state and is described by Heisenberg's uncertainty principle (∆E∆t ≥3.3x10^-15 eV⋅s).

Doppler broadening (∆V_d) results from the thermal distribution of atomic velocities along the line of sight and depends on temperature and the mass of the atoms. Collisional or pressure broadening (∆V_col) occurs when atoms collide with one another, which perturbs the energy levels and therefore the emitted frequencies.