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## QuestionPhysicsClass 12

Find the maximum frequency produced by $$30\;\text{kV}$$  electrons.

In this question we are asked to find ‘maximum frequency’ and ‘minimum wavelength’ produced by $$30\;\text{kV}$$  electrons. This is nothing, but the frequency and wavelength produced by the given energy of electrons. Energy is directly proportional to frequency, so the frequency obtained from the given energy $$($$which is the maximum possible energy$$)$$ is the maximum frequency. Similarly, Energy is inversely proportional to wavelength, so the wavelength obtained from the given energy is the minimum wavelength.
Given that, Electron potential,
$$V=30\mathit{\ kV}=30\times 10^4V$$
We know that, Energy,
$$E=\mathit{qV}$$
Where, $$V$$  is the potential and $$q$$  is the charge.
Here, $$q=e$$
Hence, Electron energy,
$$E=30\times 10^4\mathit{eV}$$
We Know that,
$$E=\mathit{h\nu }$$
Where, $$\nu$$  is the frequency and $$h=6.626\times 10^{-34}\mathit{Js}$$
Therefore, the maximum frequency of electron,
$$\nu =\frac E h=\frac{30\times 10^4}{6.626\times 10^{-34}}$$
$$=7.24\times 10^{18}\mathit{Hz}$$
Hence, $$7.24\times 10^{18}\mathit{Hz}$$  is the maximum frequency of $$X$$ -rays.