If 27.3% of a sample of silver-112 decays in 1.52 hours, what is the half-life (in hours to 3 decimal places)?

The half life of the sample of silver-112 is 3.303 hours.

Explanation:

All radioactive decay processes undergoes first order reaction.

To calculate the rate constant for first order reaction, we use the integrated rate law equation for first order, which is:

where,

k = rate constant = ?

t = time taken = 1.52 hrs

= Initial concentration of reactant = 100 g

[A] = Concentration of reactant left after time 't' = [100 - 27.3] = 72.7 g

Putting values in above equation, we get:

To calculate the half life period of first order reaction, we use the equation:

where,

= half life period of first order reaction = ?

k = rate constant =

Putting values in above equation, we get:

Hence, the half life of the sample of silver-112 is 3.303 hours.

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