Answer
$4.89\times10^{19}$ atoms.
Work Step by Step
Number of atoms at the beginning $N_{0}=5.00\times10^{22}$
Decay constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{4.20\,min}=0.165\,min^{-1}$
Time $t=42.0\,min$
$\ln(\frac{N_{0}}{N})=kt$ where $N$ is the number of atoms remaining.
$\implies \ln(\frac{5.00\times10^{22}}{N})=0.165\times42.0=6.93$
Taking the inverse $\ln$ of both sides, we have
$\frac{5.00\times10^{22}}{N}=e^{6.93}=1022.5$
Or $N= \frac{5.00\times10^{22}}{1022.5}=4.89\times10^{19}$
