Question

an electron is moving at 3.6 x 10^3 m/s. a photon with what wavelength would have the same momentum????

Answer 1

The wavelength of the photon that would have the same momentum as the electron is 202.2180996 nm

Step-by-step explanation:

The velocity of the electron, v = 3.6 × 10³ m/s

The momentum of an electron,
`p_e` = m × v

Where;

v = The mass of the electron = 9.109 × 10⁻³¹ kg

∴
`p_e` = 9.109 × 10⁻³¹ kg × 3.6 × 10³ m/s = 3.27924 × 10⁻²⁷ kg·m/s

According to the de Broglie equation, the momentum of a photon, p, is given as follows;

p = h/λ

Where;

h = 6.63 × 10⁻³⁴ J·s

λ = The wavelength of the photon

∴ λ = h/p

According to the question, we have;

p =
`p_e` = 3.27924 × 10⁻²⁷ kg·m/s

∴ λ = 6.63 × 10⁻³⁴ J·s/(3.27924 × 10⁻²⁷ kg·m/s) = 2.02180993 × 10⁻⁷ m

The wavelength of the photon, λ = 2.02180993 × 10⁻⁷ m = 202.2180993 × 10⁻⁹ m = 202.2180993 nm.