Page 8 - AAS & AES & FES 01082016_Neat

Numerical 3
Assuming a normal (Gaussian) distribution of velocities of sodium atoms in a line source

relative to the detector, calculate the width of the Doppler-broadened emissive line that
corresponds to velocities that approach or recede from the detector at a rate that

corresponds to ± 1 standard deviation on the distribution-velocity graph. Assume the
velocity at ± 1 standard deviation on the distribution-velocity graph. Assume the velocity at

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the ± 1 standard deviation points is ± 7.50×10 m/s and that the emitted wavelength with no
motion is 766.491 nm.
Ans:
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Velocity of light in vacuum = c = 2.997925×10 m/s
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Velocity of Sodium atom = v = ± 7.50×10 m/s
Wavelength of radiation = λ = 766.491 nm
f =c/λ [frequency = velocity of light/ wavelength]

For approach toward detector (+)
Atom is moving toward detector so speed of atom will increased by c + v
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Total velocity = 2.997925×10 + 7.50×10 5

= 300542500 m/s
Observed frequency f a= total velocity of light/ wavelength
-9
= 300542500 / 766.491 × 10
14
= 3.92102× 10 Hz

For recede toward (moving away from) detector (-)

Atom is moving away from detector so speed of atom will decreased by c - v
8 5
velocity = 2.997925×10 - 7.50×10
Total

= 299042500 m/s
Observed frequency f r = total velocity of light/ wavelength

-9

= 299042500 / 766.491 × 10
14

= 3.90145 × 10 Hz

The width of the Doppler-broadened emissive line that corresponds to velocities that
approach or recede from the detector = difference of frequency of approach and recede

Width of the Doppler-broadened emissive line = f a- f r
14
14
= (3.92102× 10 ) - (3.90145 × 10 )
12
= 1.95697× 10 Hz

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