Question

Sodium has a work function of 2.3eV. Given that: Planck’s constant h = 6.63 x 10^-34JS, velocity of light in vacuum, C = 3.0 x 10⁸m/s, 1 electron-volt (1eV) = 1.6 x 10^-19 C and mass of an electron, m_e = 9.1 x 10^-31kg, calculate:

1. its threshold frequency. 
2. the maximum velocity of the photoelectrons produced when the sodium is illuminated by light of wavelength 5.0 x 10^-7m.
3. the stopping potential V, with the light of this wavelength. 

Answer 1

1. hf_o = w_o
   6.63 x 10^-34f_o=2.3 x 1.6 x10^-19
   f_o = 5.55 x 10¹⁴HZ
    
2. hf = w_o + ¹/₂MV²
   h c/λ = W_o + ¹/₂MV²
   6.63 x 10^-34 x      3.0x10⁸   = 2.3 x 1.6 x 10^-19 + ¹/₂MV²
                            5.0 x 10^-7
   3.978 x 10^-19 = 3.68 x 10^-19 + ¹/₂MV^{2
   1}/₂MV² = 0.298 x 10^-19
   
    
3. eV_s = ¹/₂MV²
   1.6 x 10^-19V_s = 0.298 x 10^-19
   V_s= 0.298 x 10^-19
           1.6 x 10^-19
   =0.186Volts