KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 28 of 120

Marks: +1, -0

An electron in an electron microscope withinitial velocity

υ_0 i↖{\^}

enters a region of a stray transverse electric field

E_0 j↖{\^}

. The time taken for the change in its de-Broglie wavelength from the initial value of λ to

λ/3

is proportional 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^2_0

⇒

{qE_0}/mt=2√2v_0

t={2√2m}/{qE_0}\ \ v_0⇒t∝ 1/E_0

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