A radioactive substance has a half-life of 3 days. If a mass of 1.55g of this substance is left after decaying for 15 days, determine the original value of ...
Question 1 Report
A radioactive substance has a half-life of 3 days. If a mass of 1.55g of this substance is left after decaying for 15 days, determine the original value of the mass
Answer Details
The half-life of a radioactive substance is the time taken for half of the initial mass of the substance to decay. Let's denote the initial mass of the substance by m.
After 3 days (one half-life), the mass of the substance remaining is m/2. After 6 days (two half-lives), the mass remaining is (m/2)/2 = m/4. Similarly, after 9 days (three half-lives), the mass remaining is m/8, and after 12 days (four half-lives), the mass remaining is m/16.
After 15 days (five half-lives), we are told that there is 1.55g of the substance remaining. Therefore, we can set up the following equation:
1.55g = m/32
Solving for m gives:
m = 49.6g
Therefore, the original value of the mass of the radioactive substance was 49.6g.
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