Afirst-order reaction has a half-life of 20.0 minutes. starting with 1.00 × 1020 molecules of reactant at time t = 0, how many molecules remain unreacted after 100.0 minutes?

Half-life time of a reaction is time at which reactant concentration becomes half of its initial value.

Half-life of the first order reaction is 20 min. Rate constant can be calculated as follows:

The rate expression for first order reaction is as follows:

initial number of molecules of reactant are , time is 100 min thus, putting the values to calculate number of reactant at time 100 min,

On rearranging,

Or,

Therefore, number of molecules unreacted will be