Answer
$4.57\times 10^9~~$ alpha particles are emitted.
Work Step by Step
We can find the number of atoms remaining after $t = 50~min$:
$N = N_0~(0.5)^{t/(t_{1/2})}$
$N = (1.0\times 10^{10})~(0.5)^{50/100}$
$N = 7.07\times 10^9$
We can find the number of atoms remaining after $t = 200~min$:
$N = N_0~(0.5)^{t/(t_{1/2})}$
$N = (1.0\times 10^{10})~(0.5)^{200/100}$
$N = 2.50\times 10^9$
We can find the number of alpha particles emitted:
$(7.07\times 10^9) - (2.50\times 10^9) = 4.57\times 10^9$
$4.57\times 10^9~~$ alpha particles are emitted.
