Answer:
λ = 4.1638 10⁻⁷ m
Step-by-step explanation:
The photoelectric effect was explained by Einstein assuming that the radiation acts like particles and the equation that describes the process is
K = h f -Ф
where K is the kinetic energy of the emitted electrons, hf the energy of the photons according to Planck's equation and Ф the work function of the material
In this case they give us the kinetic energy of the electrons
K = 0.7 eV
The sodium work function is tabulated Ф = 2.28 eV
Let's find the frequency of the photons
f = (K + Ф) / h
Planck's constant is
h = 6.626 10⁻³⁴ J s (1 eV / 1.6 10⁻¹⁹ J) = 4.136 10⁻¹⁵ eV s
f = (0.7 + 2.28) / 4.136 10⁻¹⁵
f = 7.2050 10¹⁴ Hz
let's find the wavelength using the relationship between speed and frequency and wavelength
c = λ f
λ = c / f
λ = 3 10⁸ / 7.205 10¹⁴
λ = 4.1638 10⁻⁷ m