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Question

Physics Question on Dual nature of radiation and matter

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

Answer

Potential of the electrons,V=30 kV=3×104 VV=30 \,kV=3×10^4\,V
Hence,energy of the electrons,E=3×104eVE=3×10^4eV
Where,
e=Charge on an electron=1.6×10−19C=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=6.626×10−34Js=6.626×10^{−34} Js
∴v=Eh∴v=\frac{E}{h}
=1.6×10−19×3×1046.626×10−34=7.24×1018HZ=\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 7.24×1018HZ7.24×1018HZ
(b)The minimum wavelength produced by the X-rays is given as:
Hence,the minimum wavelength of X-rays produced is 0.0414 nm.