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Question 13

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:

The shortest wavelength of a photon produced by an X-ray tube corresponds to the maximum energy, where the entire kinetic energy of the accelerated electron is converted into a single photon. This gives us the relation $$eV = \frac{hc}{\lambda_{\min}}$$, so $$\lambda_{\min} = \frac{hc}{eV}$$.

Substituting the values with $$V = 1.24 \times 10^6$$ V, $$h = 6.626 \times 10^{-34}$$ J s, $$c = 3 \times 10^8$$ m/s, and $$e = 1.6 \times 10^{-19}$$ C:

$$\lambda_{\min} = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{1.6 \times 10^{-19} \times 1.24 \times 10^6} = \frac{1.9878 \times 10^{-25}}{1.984 \times 10^{-13}} = 1.002 \times 10^{-12}$$ m.

Converting to nanometres, $$\lambda_{\min} \approx 10^{-12}$$ m $$= 10^{-3}$$ nm.

The correct answer is $$10^{-3}$$ nm.

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