Question

The maximum frequency and minimum wavelength of X-rays produced by 30 kV electrons respectively is

• A. $7.24\times {10}^{18}Hz,0.041nm$
• B. $3.21\times {10}^{18}Hz,0.211nm$
• C. $5.32\times {10}^{18}Hz,0.001nm$
• D. $2.13\times {10}^{18}Hz,0.011nm$

Answer 1

Answer: (A)

$7.24\times {10}^{18}Hz,0.041nm$

Here, $V=30kV,h=6.63\times {10}^{-34}Js$
for maximum frequency of X-Ray formation:

Total Kinetic energy of electron will convert into X-Ray energy

As $K.E=eV=h{\upsilon }_{max}$

or ${\upsilon }_{max}=\frac{eV}{h}=\frac{1.6\times {10}^{-19}\times 3\times {10}^4}{6.63\times {10}^{-34}}$

${\upsilon }_{max}=7.24\times {10}^{18}Hz$

As $eV=\frac{hc}{{\lambda }_{min}}or{\lambda }_{min}=\frac{hc}{eV}$

${\lambda }_{min}=0.041\times {10}^{-9}m=0.041nm$