The half-life of Erbium-165 is 10.4 hours. After 24 hours a sample has been reduced to a mass of 2 mg. What was the initial mass of the sample, and how much will remain after 3 days?

Explanation:

Given that:

Half life = 10.4 hours

Where, k is rate constant

So,  

The rate constant, k = 0.06664 hour⁻¹

Time = 24 hours

Using integrated rate law for first order kinetics as:

Where,  

is the concentration at time t  = 2 mg

is the initial concentration = ?

So,  

Now, time = 3 days = 3*24 hours = 72 hours ( 1 day = 24 hours)

Thus,