(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I've just done a practical to plot a franck-hertz curve for mercury. There are a few post-practical questions, and i'm not sure of 2 of them:

1) estimate the contact potential

2) estimate the mean free path of an electron in mercury vapour at a temperature of 160C and vapour pressure 11.28mmHg.

2. Relevant equations

1) Contact potential = (U1+U2) - Delta U2

(Delta U2 average distance between peaks, U1 = driving voltage (constant), U2 = acclerating voltage for first peak)

2) v = (3KbT/m)^1/2

3. The attempt at a solution

1)Peaks at: 7.8V, 12.5V,17.5V, 22.4V, 27.6V. U1 = 1.9V

Average ΔU2 = [(12.5-7.8) + (17.5-12.5) + (22.4-17.5) + (27.6-22.4)]/4 eV =4.95 V

Error in ΔU2 = [±4(0.1+0.1)]/4 = ±0.2 V

First excitation potential of mercury = 5.0±0.2V

(Excitation energy of mercury = 5.0±0.2eV)

However, the first peak appears at 7.8V. This is as a result of contact potential:

Kinetic energy of the electrons at grid G2 = U1 + U2 = (7.8±0.1 + 1.9±0.1)eV = 9.7±0.2 eV

Contact potential = KE - ΔU2 = 9.7±0.2 – 5.0±0.2 = 4.7±0.4V

2) v = (3*1.38 × 10^-23 m2 kg s-2 K-1* 433.15K/9.109 × 10-31 kg)^1/2

=140308m/s

I'm not sure where to go from here, as i don't know how to use the vapour pressure to find the mean free path. Any help at all would be greatly appreciated!

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# Homework Help: Franck-Hertz curve

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