1.) How many photons strike a patient being x-rayed, where an intensity of 1.75

Question

1.)   How many photons strike a patient being x-rayed, where an intensity of 1.75 W/m2 illuminates 0.0750 m2 of her body for 0.270 s? The energy of the x-ray photons is 100 keV.

2.) The electrical power output of a large nuclear reactor facility is 920 MW. It has a 40.0% efficiency in converting nuclear power to electrical.

a.)   What is the nuclear power output in megawatts

b.) How many 235U nuclei fission each second, assuming the average fission produces 200 MeV?

c.) What mass of 235U is fissioned in one year of full-power operation?

Please show all work.

Explanation / Answer

1) total energy received = intensity * area of body * time = 1.75 * 0.075 * 0.27 = 0.0354375 J

energy of 1 photon = 100 KeV = 100 * 1000 * 1.6 * 10^-19 = 1.6 * 10^-14 J

so.. number of photon = total energy / energy of 1 photon = 0.0354375 /1.6 * 10^-14 = 2.21484375 * 10^12 photons

2)

a) let the nuclear output be E

so.. 0.4 * E = 920

so.. E= 920 / 0.4 = 2300 MW

b) no. of fission per second = total nuclear output / energy per fission = 2300 / ( 200 * 1.6 * 10^-19) = 7.1875 * 10^19 fission / sec

c)

so.. number of atoms fissioned in 1 year = 7.1875 * 10^19 * 365 * 24 * 3600 = 2.26665 * 10^27 atoms

so.. moles of atoms fissioned = 2.26665 * 10^27 / ( 6.023 * 10^23 ) = 3763.324 moles..

mass of 1 mole = 235 grams

so.. mass of 3763.3239 moles = 3763.3239 * 235 / 1000 = 884.38 kg

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