Question

Find the
(a)maximum frequency, and
(b)minimum wavelength of X-rays produced by 30 kV electrons
 

Answer 1

Potential of the electrons,\(V=30 \,kV=3×10^4\,V\)
Hence,energy of the electrons,\(E=3×10^4eV \)
Where,
e=Charge on an electron\(=1.6×10^{−19}C\)
(a)Maximum frequency produced by the X-rays=v
The energy of the electrons is given by the relation:
E=hv Where, h=Planck’s constant\(=6.626×10^{−34} Js\)
\(∴v=\frac{E}{h}\)
\(=\frac{1.6×10^{-19}×3×10^4}{6.626×10^{-34}}=7.24×10^{18}HZ\)
Hence,the maximum frequency of X-rays produced is \(7.24×1018HZ\)
(b)The minimum wavelength produced by the X-rays is given as:
Hence,the minimum wavelength of X-rays produced is 0.0414 nm.