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# Line Broadening: How do you calculate the Doppler width in MHz of these transitions?

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More line broadening: Figure 6.2 shows data from measurements of the homogeneous line width of the D_1 (6p^2 P_1/2 --> 6s^2 S_1/2) and D_2 (6p^2 P_3/2 --> 6s^2 S_1/2) transitions in Cs at 894 and 852 nm respectively.

In addition to the homogeneous broadening, in homogeneous broadening is caused by the thermal motion of the atoms. This so-called Doppler broadening has a Gaussian line shape with a full-width at half-maximum line width given by,

deltav_D = sqrt(8ln2)*sqrt((k_B)(T)/(Mc^2)) * v_0

where T is the temperature in the atoms, M their mass and v_0 the frequency emitted on the transition by a stationary atom.

a) Calculate the Doppler width in MHz of these transitions assuming that the temperature of the Cs vapour is 21C and comment on the relative magnitudes of the in homogeneous and homogeneous line widths.

b) The radioactive lifetimes of the D_1 (6p^2 P_1/2) and D_2 (6p^2 P_3/2) levels are 34.75 and 30.41 respectively. What is the natural line width of the D_1 and D_2 transitions? If your calculated value consistent with Fig. 6.2?

c) Use the data presented to deduce the rate of increase in the homogeneous line width in units of MHzTorr^-1 for each of the two transitions. Explain briefly the cause of this increase in homogeneous line width with pressure.

d) What is the mean collision time at a He pressure of 100 Torr for He-Cs collisions?

[The molar mass of Cs is 132.9g]