Question

An electron of mass M initially at rest, moves through a certain distance in a uniform electric field in timet,
A proton of mass M also initially at rest, takes time t, to move through an equal distance in this riform
electric field. Neglecting the effect of gravity, the ratio t/t, is nearly equal to​

Answer 1

Answer:

$\boldsymbol{\frac{t_2}{t_1} =\sqrt{\frac{M_p}{M_e}}}$

Explanation:

If the acceleration is a then the distance s travelled in time t is given by

$s=\frac{1}{2}at^2$

Therefore for electron

$s=\frac{1}{2}a_et_1^2$

And for Electron

$s=\frac{1}{2}a_pt_2^2$

Thus,

$\frac{t_2}{t_1} =\sqrt{\frac{a_e}{a_p}}$  .......... (1)

Force on electron in an electric field E

$F_e=eE$

Thus the acceleration of the electron if its mass is $M_e$

$a_e=\frac{F_e}{M_e} =\frac{eE}{M_e}$

Similarly the acceleration of the proton

$a_p=\frac{F_e}{M_p} =\frac{eE}{M_p}$

Therefore,

$\frac{a_e}{a_p}=\frac{M_p}{M_e}$

Therefore, from (1)

$\frac{t_2}{t_1} =\sqrt{\frac{M_p}{M_e}}$

Answer 2

Answer:

√ ae/ ap = √ mp/me

Explanation:

Mass of the electron = M (Given)

Mass of the proton = M (Given)

Time = t (Given)

Electrostatic force, FE = eE (for both electron and proton)  

But acceleration of electron, ae =FE/me whereas -  

acceleration of proton, ap = FE/mp

S = 1/2at²1 = 1/2apt²2  

Therefore,

t2/t1 = √ ae/ ap

t2/ t1 = √ ae/ ap = √ mp/me

Thus, the ratio is nearly equal to - √ ae/ ap = √ mp/me