Question

A 54.1 mg sample of sodium perchlorate contains radioactive chlorine-36 (whose atomic mass is 36.0 amu).

1. 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.

Answer 1

We know all nuclear reactions follow first order kinetic.

Rate of disintegration = lN

Here   l is rate constant

N is number of radioactive nuclides

Lets find initial amount of N

Initial amount is found by using mass of perchlorate

Calculation of moles of Cl in sodium perchlorate.

Formula for sodium perchlorate NaClO4

In one mole of sodium perchlorate contains one mole of Cl so we can use this mole ratio to get moles of Cl

Moles of Cl = moles of NaClO4 x 1 mol Cl / 1 mol sodium perchlorate

Moles of sodium perchlorate

= ( 54.1 x 10^-3 g / molar mass of sodium perchlorate x 1 mol Cl / 1 mol sodium perchlorate

= 0.000442 mol Cl

Calculation of atoms of radioactive Cl

= 0.000442 mol x 6.022 E23 Cl radioactive / 1 mol

N = 2.66 E20 Cl atoms.

Calculation disintegration constant (l )

l = 0.693 / t ½

= 0.693 / (3.0E 5 yr)

= 2.31 E-6 per yr

Lets calculated rate

Rate of disintegration = 2.31 E-6 per year x 2.66 E20 Cl atoms.

= 6.14 E14 d per year

We convert it to per s

= 6.14 E14 (d / year ) x (1 year/ 365*24*60*60 s )

= 4.68 E8 dps