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Archy [21]
3 years ago
9

When studying radioactive​ material, a nuclear engineer found that over 365​ days, 1,000,000 radioactive atoms decayed to 973 co

mma 635 radioactive​ atoms, so 26 comma 365 atoms decayed during 365 days. a. Find the mean number of radioactive atoms that decayed in a day. b. Find the probability that on a given​ day, 51 radioactive atoms decayed.
Mathematics
1 answer:
HACTEHA [7]3 years ago
4 0

Answer:

A. number of decayed atoms = 73.197

Step-by-step explanation:

In order to find the answer we need to use the radioactive decay equation:

N(t)=N0*e^{kt} where:

N0=initial radioactive atoms

t=time

k=radioactive decay constant

In our case, when t=0 we have 1,000,000 atoms, so:

1,000,000=N0*e^{k*0}

1,000,000=N0

Now we need to find 'k'. Using the provied information that after 365 days we have 973,635 radioactive atoms, we have:

973,635=1,000,000*e^{k*365}

ln(973,635/1,000,000)/365=k

-0.0000732=k

A. atoms decayed in a day:

N(t)=1,000,000*e^{-0.0000732t}

N(1)=1,000,000*e^{-0.0000732*1}

N(1)= 999,926.803

Number of atoms decayed in a day = 1,000,000 - 999,926.803 = 73.197

B. Because 'k' represents the probability of decay, then the probability that on a given day 51 radioactive atoms decayed is k=0.0000732.

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