91Ó°ÊÓ

A substance's volume is the amount of space it occupies.

Number of alpha particles produced in \(1\)year \( = 1.16 \times {10^{18}}\) particles

First, we convert the number of particles to number of moles produced.

We know that, \(1\;{\rm{mol}}\) of any substance contains \(6.022 \times {10^{23}}\) particles. So, moles of the alpha particles produced is

\(\begin{aligned}{}n &= \frac{{1.16 \times {{10}^{18}}{\rm{ particles }}}}{{6.022 \times {{10}^{23}}{\rm{ particles }}/{\rm{mol}}}}\\ &= 1.93 \times {10^{ - 6}}\;{\rm{mol}}\end{aligned}\)

We must rearrange \(PV = nRT\) to solve for \(P:P = \frac{{nRT}}{V}\)

If we choose to use \(R = 8.314{\rm{kPaLmo}}{{\rm{l}}^{ - 1}}\;{{\rm{K}}^{ - 1}}\), then the amount must be in moles, temperature must be in kelvin, and volume must be in \(L\).

Converting into the right units:

Therefore, the calculated pressure is \(3.83 \times {10^{ - 2}}{\rm{kPa}}\).