Solve Half-Life Problem: Find # Atoms Decaying in 12 Days

In summary, the conversation discusses a multiple choice question involving a radioactive source with a half-life of 3 days and 1.6×10^20 atoms of a radioactive isotope. The question asks how many atoms will decay in 12 days, with the options ranging from 1.0×10^19 to 1.5×10^20. The conversation also mentions a strategy of using proportionality to find the answer, but the suggested answer of 6.4×10^20 is not one of the given options and is not physically reasonable. The conversation ends with a request for help and a clarification of the question.
  • #1
VjStylz
2
0
Missing homework template, originally posted in different forum.
Alright so i have exams in a matter of days and stumbled upon this multiple choice question

7. A radioactive source has 1.6×10^20 atoms of a radioactive isotope, with a half-life of 3 days. How many atoms will decay in 12 days?
A. 1.0×10^19
B. 1.2×10^20
C. 4.0×10^19
D. 1.5×10^20

So my first obvious choice of discourse was to attack the question in terms of proportionality:

3 = 1.6 * 10^20
12 = x
And my answer was : 6.4 * 10^20, Which is not even close to any of the above options. I reall don't know what to do from here. Please Help, Thanks in advance
 
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  • #2
VjStylz said:
3 = 1.6 * 10^20
This statement makes absolutely no sense. Three is not equal to 160000000000000000000.

You are also stating that more atoms have decayed than you had from the beginning, which is clearly not physically reasonable.

If the half life is 3 days, how many atoms do you hav left after 3 days? How many of those do you have left after another 3 days?
 

1. How do you calculate the number of atoms decaying in a given time period?

In order to calculate the number of atoms decaying in a given time period, we can use the half-life formula: N(t) = N0(1/2)^(t/t1/2), where N(t) represents the remaining number of atoms, N0 represents the initial number of atoms, t represents the time passed, and t1/2 represents the half-life of the substance.

2. What is the half-life of a substance?

The half-life of a substance is the amount of time it takes for half of the atoms in a sample to decay. This value is unique to each substance and can range from fractions of a second to billions of years.

3. How do you find the initial number of atoms in a sample?

The initial number of atoms in a sample can be found by dividing the current number of atoms by the fraction of atoms remaining after one half-life. This can be represented by the formula: N0 = N(t)/ (1/2)^(t/t1/2).

4. Can the half-life of a substance change?

The half-life of a substance is a constant value that does not change. It is determined by the properties of the substance and remains the same regardless of the size or conditions of the sample.

5. How can the half-life problem be applied in real-world scenarios?

The half-life problem can be applied in various fields such as radiocarbon dating, medical imaging, and nuclear energy. It allows us to determine the age of objects, track the decay of radioactive substances, and understand the rate of nuclear reactions.

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