How many days will it take for one half of the original amount of a radioactive substance to decay if the half-life is 30 days?
a. 3 days
b. 15 days
c. 30 days
d. 60 days

C. 30 years

Explanation:

Half life of a radioactive substance is defined as the time taken by the substance to decay to half of its original value.

The number of days it will take for one half of the original amount of a radioactive substance to decay given the half life of 30 years will be that same 30years according to the half life definition.

According to the formula for half life t1/2 = ln2/¶ where ¶ is the decay constant.

¶ = ln2/t1/2

¶ = ln2/30

¶ = 0.023

Using the radioactivity formula to get the time it will take 1/2 of the original amount to decay, we have;

N/No = e^-¶t where

N/No is the fraction of amount decayed at time t i.e 1/2

Substituting the given values in the equation, we have;

1/2 = e^-0.023t

ln1/2 = lne^-0.023t

ln1/2 = -0.023t

t = ln0.5/-0.023

t = 30years.