Through how many volts of potential difference must an electron, initially at rest, be accelerated to achieve a wave length of 0.27nm? A) 4.6 V

B) 0.046 V

C) 0.27 V

D) 4.6 MV

E) 4.6 kV

20.7 volts

Explanation:

m = mass of electron = 9.1 x 10⁻³¹ kg

λ = wavelength of electron = 0.27 x 10⁻⁹ m

v = speed of electron

Using de-broglie's hypothesis

λ m v = h

(0.27 x 10⁻⁹) (9.1 x 10⁻³¹) v = 6.63 x 10⁻³⁴

v = 2.7 x 10⁶ m/s

ΔV = Potential difference through which electron is accelerated

q = charge on electron = 1.6 x 10⁻¹⁹ C

Using conservation of energy

(0.5) m v² = q ΔV

(0.5) (9.1 x 10⁻³¹) (2.7 x 10⁶) ² = (1.6 x 10⁻¹⁹) ΔV

ΔV = 20.7 volts