The surface of sodium metal is irradiated with radiation of wavelength x nm. The kinetic energy of ejected electrons is 2.8 10⁻²⁰ J. The work function of sodium is 2.3 eV. The value of x is _____ 10^2 nm. (Nearest integer) (Given: h = 6.6 10⁻³⁴ J s; 1 eV = 1.6 10⁻¹⁹ J; c = 3.0 10^8 m s ⁻¹ )

Step-by-step solution

The work function of sodium in Joules is: = 2.3 1.6 10⁻¹⁹ = 3.68 10⁻¹⁹ J The kinetic energy of the ejected electrons is: K = 2.8 10⁻²⁰ = 0.28 10⁻¹⁹ J Using the photoelectric equation, the energy of the incident photon is: E = + K E = 3.68 10⁻¹⁹ + 0.28 10⁻¹⁹ = 3.96 10⁻¹⁹ J The wavelength of the incident radiation is calculated using E = hc : = hc E = 6.6 10⁻³⁴ 3.0 10^8 3.96 10⁻¹⁹ = 19.8 10⁻²⁶ 3.96 10⁻¹⁹ = 5 10⁻⁷ m Converting the wavelength to nanometers: = 500 10⁻⁹ m = 500 nm Given that the wavelength is x nm, we ge