An X-ray tube produces a continuous spectrum | vedclass

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(A) The energy of a photon is given by the formula $E = \frac{hc}{\lambda}$.Given, $\lambda = 45 	imes 10^{-2} 	ext{ Å} = 45 	imes 10^{-12} 	ext{

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$27$

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(A) The energy of a photon is given by the formula $E = \frac{hc}{\lambda}$.Given, $\lambda = 45 	imes 10^{-2} 	ext{ Å} = 45 	imes 10^{-12} 	ext{ m}$.Substituting the values: $E = \frac{6.62 	imes 10^{-34} 	imes 3 	imes 10^8}{45 	imes 10^{-12}} 	ext{ J}$.$E = \frac{19.86 	imes 10^{-26}}{45 	imes 10^{-12}} 	ext{ J} = 0.4413 	imes 10^{-14} 	ext{ J}$.To convert energy into $eV$, divide by the charge of an electron $(1.6 	imes 10^{-19} 	ext{ C})$:$E_{eV} = \frac{0.4413 	imes 10^{-14}}{1.6 	imes 10^{-19}} 	ext{ eV} \approx 0.2758 	imes 10^5 	ext{ eV} = 27,580 	ext{ eV}$.Rounding to the nearest given option, the value is $27,500 	ext{ eV}$.

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ Å}$. The maximum energy of a photon in the radiation in $eV$ is (in $27,500$). $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$.

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