# Calculation of number of Uranium-235 nuclei

In a problem, I'm supposed to calculate the number of Uranium-235 nuclei in 10^4 Kg of Uranium. The answer book gives

Number of U-235 nuclei = (10^4)*(1000/238)(6*10^23)(0.02) = 5*10^26

I don't know where the factor 6*10^23 and (1000/238) come from. The 0.02 come from the fact that 2% of Uranium is U-235 and the rest is U-238. 10^4 is the mass. Is the number 238 somehow associated with U-238? Could you please explain, why this calculation includes (1000/238) and 6*10^23? Thank you.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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Molecular weight of U-238 = 238 Grams

Hence, Number of Moles in 10^4 kg of Uranium = 10^4 * 1000 (Grams) / 238 (Grams)

Now, Number of Nuclei in 1 mole = Avagadro Number = 6.023*10^23(exactly) = 6*10^23 (rounded)

Now since only 2% of Uranium is U-235 we now get,

Number of U-235 Nuclei in 10^4 kg 0f Uranium = (10^4)*(1000/238)(6*10^23)(0.02) = 5*10^26

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https://brainmass.com/physics/conservation-laws/calculation-number-uranium-nuclei-186051