A54.3 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 is naturally occurring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? the half-life of chlorine-36 is 3.0×105 yr.

Explanation:

Calculation of the moles of sodium perchlorate as:-

Mass = 54.3 mg

Also, 1 mg = 0.001 g

So, Mass =

Molar mass of sodium perchlorate = 122.44 g/mol

The formula for the calculation of moles is shown below:

Thus,

Also, given that it contains 29.6 % of the radioactive Chlorine

So, Moles of radioactive chlorine in the sample =

1 mole of Chlorine contains   atoms of chlorine

So,

0.000131276 mole of Chlorine contains   atoms of chlorine

Atoms of radioactive chlorine in the sample =

Given that:

Half life = year

1 year = s

Half life = s = 9462000000000 s

The expression for half-life is:-

Where, k is rate constant

So,  

The rate constant, k = s⁻¹

Disintegration is:-

Disintegrations per second = Rate constant*Number of atoms = =

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