Question

An electron is accelerated from rest through a potential difference of 100 V. Find:

1. the wavelength associated with
2. the momentum and
3. the velocity required by the electron.

Answer 1

(i) Wavelength = λ = `"h"/sqrt(2  "meV")`

λ = `(6.6 xx 10^-34)/sqrt(2 xx 9.1 xx 10^-31 xx 1.6 xx 10^-19 xx 100)`

= 1.2 × 10⁻¹⁰ m

∴ λ = 1.2 Å

(ii) Momentum = p = `"h"/λ`

p = `(6.6 xx 10^-34)/(1.2 xx 10^-10)`

∴ p = 5.5 × 10⁻²⁴ kg m/s

(iii) Momentum = p = mv

∴ Velocity = v = `"p"/"m"`

= `(5.5 xx 10^-24)/(9.1 xx 10^-31)`

= 6 × 10⁶ m/s