Answer:
3.83 × 10⁻¹⁹ J; 518 nm
Step-by-step explanation:
The equation for the photoelectric effect is
hf = Φ + KE
Data:
λ = 300 nm = 300 × 10⁻⁹ m
KE = 1.68 × 10⁵ J/mol
Calculations:
Part 1. Minimum energy to remove an electron
(a) Calculate the energy of the photon
fλ = c
f = c/λ Divide each side by λ
E = hf
E = hc/λ
E = (6.626× 10⁻³⁴ × 2.998 × 10⁸)/(300 × 10⁻⁹)
E = 6.622 × 10⁻¹⁹ J
(b) Calculate the KE of one electron
KE = 1.68 × 10⁵ × 1/(6.022 × 10²³)
KE = 2.790 × 10⁻¹⁹ J
(c) Calculate the work function
hf = Φ + KE Subtract KE from each side
Φ = 6.622 × 10⁻¹⁹ - 2.790 × 10⁻¹⁹
Φ = 3.83 × 10⁻¹⁹ J
The minimum energy to remove an electron from a sodium atom
is 3.83 × 10⁻¹⁹ J.
Part 2. Maximum wavelength to remove an electron
The photon must have just enough energy to overcome the work function and leave the electron with zero kinetic energy.
E = Φ
hc/λ = Φ Multiply each side by λ
hc = Φ λ Divide each side by Φ
λ = hc/ Φ
λ = (6.626 × 10⁻³⁴ × 2.998 × 10⁸)/(3.83 × 10⁻¹⁹)
λ = 5.18 × 10⁻⁷ m Convert to nanometres
λ = 518 nm
The maximum wavelength that will cause an electron to move is 518 nm.
