Question

An X-ray operates at 30000V and the current through it is 2mA. Given that the charge of an electron is 1.6 x 10^-19C, h = 6.63 x 10^-34JS, speed of light, C = 3.0 x 10⁸m/s, calculate:-

1. the maximum kinetic energy of the electrons when hitting the target. 
2. the number of electrons hitting the target per second.
3. the minimum wavelength of the X-rays emitted.

Answer 1

1.  Ke = ½MV² = eV
   = 1.6 × 10^-19 × (30,000)²
   = 1.44 × 10^-10J
    
2. 
   I=ne
   2 x 10^-3 = n x 1.6 x 10^-19
   n= 2x 10^-3
       1.6 x 10^-19
   =1.25 x 10¹⁶ electrons
    
3. 
   hf_max = eV But f_max= ^e/_λmin
   h ^e/_λmin = eV
   λmin =hc/eV 
   = 6.63 x 10-34 x 3 x 10⁸
         1.44 x 10^-10
   = 1.38 x 10^-15m