The wavelength of electrons accelerated from rest through a potential difference of $40 kV$ is $X \times 10^{- 12} m .$ The value of $x$ is. (Nearest integer)
Given: Mass of electron $= 9.1 \times 10^{- 31} kg$
Charge on an electron $= 1.6 \times 10^{- 19} C$
Planck's constant $= 6.63 \times 10^{- 34} Js$

Question

The wavelength of electrons accelerated from rest through a potential difference of $40 kV$ is $X \times 10^{- 12} m .$ The value of $x$ is. (Nearest integer)

Given: Mass of electron $= 9.1 \times 10^{- 31} kg$

Charge on an electron $= 1.6 \times 10^{- 19} C$

Planck's constant $= 6.63 \times 10^{- 34} Js$

TestHub · Accepted Answer

De-broglie-wave length of electron: λ e = h 2 m ( KE ) ∵ e - is accelerated from rest ⇒ KE = q × V λ = h 2 mqv = 6 . 63 × 10 - 34 2 × 1 . 6 × 10 - 19 × 9 . 1 × 10 - 31 × 40 × 10 3 = 0 . 614 × 10 - 11 m = 6 . 14 × 10 - 12 m Nearest integer = 6 OR λ = 12 . 3 V Å = 12 . 3 200 = 6 . 15 × 10 - 12 m Ans. is 6

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