# One uranium atom has a mass of 3.95 x 10^-22 grams. How would you work out an estimate for the number of uranium atoms in 1kg of uranium?

May 2, 2017

Well, we would calculate the quotient:

$\frac{1 \times {10}^{3} \cdot g}{3.95 \times {10}^{-} 22 \cdot g} = 2.53 \times {10}^{24}$ $\text{uranium atoms}$

#### Explanation:

Alternatively, we could work out the molar quantity, knowing that $\text{Avogadro's number}$, ${N}_{A}$ uranium atoms have a mass of $238.03 \cdot g$. We thus speak of the molar mass of uranium as $238.03 \cdot g \cdot m o {l}^{-} 1$.

And thus $\text{moles of uranium} = \frac{1000 \cdot g}{238.03 \cdot g \cdot m o {l}^{-} 1} = 4.20 \cdot m o l$.

And then multiply this molar quantity by $\text{the Avocado number}$:

4.20*cancel(mol)xx6.022xx10^23*cancel(mol^-1)=??

Should the numbers be the same? Are the numbers the same?