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A certain substance has a half-life of 4 minutes. A fresh sample of the substance weighing 90 mg was obtained. After how many minutes will there be 23 mg of the substance remaining?

Respuesta :

The half life of a substance is the time i takes for the radioactive component for a substance to decay or disintegrate to half of its initial size.

  • We are to find the time (number of minutes) is would take for 23 mg of the substance to be remaining.

  • The formula for time is written as:

t =  [t1/2 x In(Nt/No)]  / In 2

where:

t1/2 = Half life = 4 minutes

No = Initial quantity of the sample = 90 mg

Nt = Amount of the sample left = 23 mg

t =  time elapsed = ?

Hence,

t = [4 x In (23/90)] / -In 2

t = 7.8731645610906 minutes

Approximately to the nearest hundredth = 7.87 minutes

Therefore, there will be 23mg of substance remaining after 7.87 minutes.

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