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A discharge tube contains helium at a lo...

A discharge tube contains helium at a low pressure. A large potential difference is applied across the tube. Consider a helium atom that has just been ionized 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 the ionization.`

Text Solution

Verified by Experts

Let the two particles have charge 'q'
Mass of electron `m_0 = 9.1 xx (10^-31) kg`
` Mass of proton m_p = 1.67 xx (10^-27) kg `
` Force experienced by Electron = qE `
` [Electric field E]`
` Acceleration = qE/m_0`
` For time dt S_e= 1/2 xx qE/m_0 xx dt^2 ` .......(1)
` For the positive ion, acceleration `
` =qE/(4xxm_p)`
` S_p = 1/2 xx qE/(4xx m_p) xx dt^2 ......(2)`
` S_e/S_p = 4m_p/m_e `
` = (4 xx 1.67 xx (10^-27))/(9.1 xx (10^-31) `
` = 0.73406 xx (10^-31) = 7340.6`.
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