Question

A 228 mL sample of an aqueous solution contains 2.00 %MgCl2 by mass (molar mass of MgCl2 is 96.9 g/mol). Exactly one-half of the magnesium ions are Mg−28, a beta emitter with a half-life of 21 hours.

What is the decay rate of Mg−28 in the solution after 4.00 days? (Assume a density of 1.02 g/mL for the solution.)

Express your answer using two significant figures(atoms/day)

Answer 1

Given:

We are given half life of Mg-28 = 21 hrs.

We have to find the rate of decay rate after 4.0 days.

Given density of the solution is 1.02 g/mL

Solution :

Here we use density and mass percent to get mass of the solution and mass of the MgCl2 and from the mass of MgCl2 we can get moles of it.

From the moles of MgCl2 in the solution we can get moles of Mg2+ . From the moles of Mg2+ we can get number of ions of it.

These are the initial ions that present in the solution.

Since radioactive decay obeys first order kinetics law. So we can use first order integrated equation and half life equation to get rate decay after 4.00 days.

Lets first find out decay constant and then by using it we can get amount of Mg2+ after 4.0 days.