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Electric Current through Gases — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsElectric Current through Gases4 Marks
Question
A discharge tube contains helium at low pressure. A large potential difference is applied across the tube. Consider a helium atom that has just been ionised due to the detachment of an atomic electron. Find the ratio of the distance travelled by the free electron to that by the positive ion in a short time dt after ionisation.
✓

Answer

Let the two particles have charge ‘q’

Mass of electron ma = 9.1 × 10-31kg

Mass of proton mp = 1.67 × 10-27kg

Electric field be E

Force experienced by Electron = qE

$\text{accln.}=\frac{\text{qE}}{\text{m}_\text{e}}$

For time dt

$\text{S}_\text{e}=\frac{1}{2}\times\frac{\text{qE}}{\text{m}_\text{e}}\times\text{dt}^2\ ....(\text{i})$

For the positive ion,

$\text{acceleration}=\frac{\text{qE}}{4\times\text{m}_\text{p}}$

$\text{S}_\text{p}=\frac{1}{2}\times\frac{\text{qE}}{4\times\text{m}_\text{p}}\times\text{dt}^2\ ....(\text{ii})$

$\frac{\text{S}_\text{e}}{\text{S}_\text{p}}=\frac{4\text{m}_\text{p}}{\text{m}_\text{e}}=7340. 6$

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