Find the: (a) Maximum frequency, and (b) The minimum wavelength of X-rays produced by $30 \mathrm{kV}$ electrons.

Home » Find the: (a) Maximum frequency, and (b) The minimum wavelength of X-rays produced by electrons.

Find the: (a) Maximum frequency, and (b) The minimum wavelength of X-rays produced by $30 \mathrm{kV}$ electrons.

Electron potential is given as $\mathrm{V}=30 \mathrm{kV}=\mathbf{3} \times \mathbf{1 0}^{4} \mathrm{~V}$

Hence, electron energy will be $\mathbf{E}=\mathbf{3} \times \mathbf{1 0}^{4} \mathrm{eV}$

Where, $e=$ Charge on one electron $=1.6 \times 10^{-19} \mathrm{C}$

(a) Maximum frequency by the $X$ -rays $=v$

Energy of the electrons can be written as,

$E=$ hv

Where,

$h=$ Planck’s constant $=\mathbf{6 . 6 2 6} \times 10^{-34} \mathrm{~J} \mathrm{~s}$

Therefore, $v=\frac{E}{h}$

$=\frac{1.6 \times 10^{-19} \times 3 \times 10^{4}}{6.626 \times 10^{-34}}=7.24 \times 10^{18} \mathrm{~Hz}$

$7.24 \times 10^{18} \mathrm{~Hz}$ is the maximum frequency of the $X$ -rays.

(b) The minimum wavelength is given as,

$\lambda=\frac{c}{v}$

$=\frac{3 \times 10^{8}}{7.24 \times 10^{18}}=4.14 \times 10^{-11} \mathrm{~m}=0.0414 \mathrm{~nm}$

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