A 53.8-mg sample of sodium perchlorate contains radioactive chlorine-36 (whose atomic mass is 36.0 amu). If 29.6% of the chlorine atoms in the sample are chlorine-36 and the remainder are naturally occurring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half-life of chlorine-36 is 3.0 × 105yr.

I am trying to find the correct number of radioactive Cl nuclei, but am uncertain if the procedure I used is correct.

n=m/M=(53.8mg/(1000g/mg))/122.44g/mol
=4.39398889...x10^-4mol

At this point, I am not whether this molar quantity of NaClO4 is equivalent to that Cl overall or if I am supposed to take the fraction of the molecule that is Cl and multiply by the calculated molar value (which would be 1/6). once I have clarified this I should be fine.

I don't think the molar mass of the 58.3 mg sample is 122.44 nor do I think you can calculate what it is. The NaClO4 contains Cl35, Cl36, Cl37in this sample. You know the percent Cl36 but you don't know the percentages of the other two (except of course in naturally occurring NaClO4.) So I think you must start with 58.3 mg NaClO4 x 0.296 = ?mg Cl-36 and you convert that to atoms of Cl-36. Knowing atoms you can go to dps.

To determine the correct number of radioactive chlorine (Cl-36) nuclei in the 53.8-mg sample of sodium perchlorate, you need to consider the information given about the percentage of chlorine atoms in the sample that are Cl-36.

First, let's calculate the molar quantity of sodium perchlorate (NaClO4) in the sample:

n = m/M
= (53.8 mg / (1000 g/mg)) / 122.44 g/mol
≈ 4.39398889 x 10^-4 mol

Now, let's address the fraction of chlorine atoms that are Cl-36. The problem states that 29.6% of the chlorine atoms in the sample are Cl-36, while the remaining atoms are naturally occurring nonradioactive chlorine atoms.

To determine the number of Cl-36 nuclei, we need to consider the molar quantity of sodium perchlorate calculated above. Since there is one chlorine atom in each sodium perchlorate (NaClO4) molecule, the molar quantity of Cl-36 will be the same as the molar quantity of sodium perchlorate if all the chlorine atoms were Cl-36.

However, we know that only 29.6% of the chlorine atoms are Cl-36. Therefore, we need to multiply the molar quantity by the fraction of Cl-36 atoms:
n(Cl-36) = 29.6% x n
= 29.6% x 4.39398889 x 10^-4 mol

Now you can calculate the number of disintegrations per second based on the radioactive decay of Cl-36.

The half-life of Cl-36 is given as 3.0 x 10^5 years. To convert this to seconds, use the fact that 1 year has approximately 3.15 x 10^7 seconds (taking into account leap years):
T = 3.0 x 10^5 years x (3.15 x 10^7 seconds/year)
≈ 9.45 x 10^12 seconds

Now, you can use the radioactive decay formula to calculate the number of disintegrations per second:

N = N0 * (1/2)^(t/T)

Where N0 is the initial number of Cl-36 nuclei, t is the time elapsed, and T is the half-life.

Using the calculated molar quantity of Cl-36 (n(Cl-36)), you can convert it to the number of Cl-36 nuclei (N0) by multiplying it by Avogadro's number (6.022 x 10^23 nuclei/mol).

N0 = n(Cl-36) x Avogadro's number

Finally, you can substitute the values into the radioactive decay formula to find the number of disintegrations per second.