Final answer:
To find the number of alpha particles emitted, convert the specific activity into disintegrations per second, multiply by the mass of the sample to get total activity, and then convert to the total number of decays in one hour.
Step-by-step explanation:
The student's question involves calculating the number of alpha particles emitted by a radioactive sample based on its specific activity. The specific activity is given as 7.29 x 10^-4 Ci/g, and we are asked to find out how many alpha particles a 75.0 mg sample emits in one hour.
First, we need to convert the specific activity into disintegrations per second (decays/s) by using the conversion factor 1 Ci = 3.7 x 10^10 decays/s. Then, we calculate the total activity of the sample by multiplying the specific activity by the mass of the sample. Finally, we convert the activity per second into the total number of decays (alpha particles emitted) in one hour by multiplying by the number of seconds in an hour (3600 seconds).