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 )
A. A
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 get x = 500. Expressing x in the required format: x = 5 10^2 The value to be filled in the blank is 5. Answer: 5
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