JEE Mains Model Paper 4

According to the problem de-Broglie wavelength of electron at time t = 0 is λ0 =

h

mv0

Electrostatic force on electron in electric field is

→

Fe

= -e

→

E

= -e E0

^

j

The acceleration of electron

→

a

=

→ F

m

= −

eE0

m

^

j

It is acting along negative y-axis. The initial velocity of electron along x-axis,
vx0 = v0

^

i

.
Now considering y-direction. Initial velocity of electron along y-axis vy0 = 0
Velocity of electron after time t along y-axis vy = 0 + (−

eE0

m

^

j

)t = -

eE0

m

t

^

j

Magnitude of velocity of electron after time t is v = v0√1+

e2E02t2

m2v02

De-Broglie wavelength λ =

h

mv

⇒ λ =

λ0

√1+ e2E02t2 m2v02