Question

An electron and a proton are moving in same electric field which will have Greater acceleration?

Answer 1

We know that

F = m × a ---- ( i ) Also

F = q × E ----( ii )

from ( i ) and (ii)

m × a = q × E

=> a =( q × E ) / m

As magnitude of Charge on electron and proton is same ( i.e 1.6 x 10^19 C ) and E is given same for both the charges....But mass of both the particke is different..

Proton is much heavier particle than electron

thus m = mass of an epectron , M = mass of proton

=> M >> m => M / m >> 1 ---- ( iii )

a1 = acceleration of electron = ( q × E ) / m

a2 = accelersation of proton = ( q × E ) /M

a1

a1 : a2 = a1 / a2 = [ ( q × E ) / m ] / [ ( q × E ) / M ]

=> a1 / a2 = M / m >> 1 ---- using ( iii )

=> a1 / a2 >> 1 => a1 >> a2

Thus acceleration of electron would be much greater thab that of proton