KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 32 of 120

Marks: +1, -0

A particle of charge q and mass m enters a region of a transverse electric field of

E_0j ↖{\^}

with initial velocity

V_0i ↖{\^}

. The time taken for the change in the de Broglie wavelength of the charge from the initial value of

λ_0 \to λ_0/3

isproportional to

Solution:

λ=h/{mv}⇒λ∝ 1/v

v=√{v^2_y+v_0^2}

v_y = u_y + a_yt

v_y=0+{qE_0}/mt

(3v_0) =√{v^2_y+v_0^2}

⇒

v^2_y=8v_0^2

⇒

{qE_0}/mt=2√2v_0

⇒

t={2√2m}/{qE_0}v_0

t ∝ m/q

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