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49.8 hours

Step-by-step explanation:

Given data,

Initial amount of sodium-24 = I = 30 mg

Half life duration = d = 15 hours

Number of half life = n = ?

Remaining amount = A = 3 mg

The relation between the Initial amount, remaining amount and number of half life is calculated using:  A = I(0.5)^n

By putting values in the equation above, we get

3 = 30(0.5)^n

3/30 = 0.5^n

1/10 = 0.5^n

Taking log on both side

ln(1/10) = ln(0.5)^n

-ln(10) = n*ln(0.5)    as ln(1/x) = -ln(x)

-ln(10)/ln(0.5) = n

3.32 = n

n = 3.32

So it would take 3.32 number of half life for the 30 mg substance to be converted in 3 mg.

Duration of each half life d = 15 hours thus the total time required is

n*d

15*3.32

=> 49.8 hours

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step-by-step explanation:

step-by-step explanation: