The work function of cesium atom is 1.9 eV. Converting the unit in J.
1.9eV × 1.602 × 10⁻¹⁹J/eV = 3.04 × 10⁻¹⁹J
The threshold frequency is
3.04 × 10⁻¹⁹ = hν₀
ν₀ = 3.04 × 10⁻¹⁹ / 6.626 × 10⁻³⁴ = 4.59 × 10¹⁴Hz.
The threshold wavelength is
λ₀ = c/ν₀ = 3.0 × 10⁸ / 4.59 × 10¹⁴ = 6.54 × 10⁻⁷m.
The energy of radiated light is
E = hc/λ = 6.626 × 10⁻³⁴ × 3 × 10⁸ / 500 × 10⁻⁹ = 3.98 × 10⁻¹⁹J
The kinetic energy of ejected electron is
K.E = 3.98 × 10⁻¹⁹ - 3.04 × 10⁻¹⁹ = 9.4 × 10⁻²⁰J
½mv² = 9.14 × 10⁻²⁰J
v = √(2K.E/m) = √(2 × 9.14 × 10⁻²⁰ / 9.1 × 10⁻³¹)= 4.54 × 10⁵m/s