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An electron and proton are detected in a...

An electron and proton are detected in a cosmic ray experiment, the first with kinetic energy 10 KeV and the second with 100 KeV. Which is faster, the electron or the proton? Obtain the ratio of their speeds
(electron mass : `9.11 xx 10^(-31)kg : `proton mass : `1.67xx 10^(-27) kg : 1 e v = 1.6 xx 10^(-19) J)`

Text Solution

Verified by Experts

Here `K_e = 10 eV and K_(p ) = 100 KeV `
` m_(e ) = 9.11 xx 10^(-31) Kg and m_p = 1.67 xx 10^(-27 ) Kg `
as ` K =1/2 mv ^2 ` or `v= sqrt((2K )/( m))`
hence ` (v_p )/( V_p) = sqrt((K_e )/(K_p) xx (m_p)/(m_c))= sqrt((10 k e )/( 100 ke V ) xx ( 1.67 xx 10^(-27 ) kg )/( 9.11 xx 10^(-31) kg ) )= 13.54`
` V_(e ) = 1354 v_P`
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