Calculating Half-Life: 0.48g to 0.003g

  • Thread starter Zoheb Imran
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In summary, the half-life of a radioactive substance is 5 hours. A sample is tested and found to contain 0.48g of the substance. To calculate how much of the substance was present in the sample 20 hours before it was tested, we must calculate backwards in time using the half-life. After 4 half-lives, there would have been 0.003g of the substance present in the sample. Therefore, 20 hours before the sample was taken, there would have been 0.003g of the substance.
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Zoheb Imran
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Homework Statement



The Half-life of a radioactive substance is 5 hours. A sample is tested and found to contain 0.48g of the substance.
How much of the substance was present in the sample 20 hours before the sample was tested?

Homework Equations





The Attempt at a Solution


i did like this...

20/5 = 4 half life

0.48---->0.24--->0.12--->0.06--->0.003g amount of substance was present.

am i right?
 
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  • #2
Zoheb Imran said:
How much of the substance was present in the sample 20 hours before the sample was tested?

Right idea, but you want the other direction in time...
 
  • #3
why the other direction? can you please explain? that's where i am having problem...in calculating...
 
  • #4
Zoheb Imran said:
why the other direction? can you please explain? that's where i am having problem...in calculating...

You are calculating forward in time when you used the half-life. So you are figuring out how much of the radioactive material is left after it was sampled. The question asks you to figure out how much of the material was present before the sample was made...
 
  • #5
thanks!
 

FAQ: Calculating Half-Life: 0.48g to 0.003g

How do I calculate half-life for a substance?

The formula for calculating half-life is: t1/2 = (ln 2) / λ, where t1/2 is the half-life, ln 2 is the natural logarithm of 2 (approximately 0.693), and λ is the decay constant.

What is the decay constant?

The decay constant, denoted as λ, is a measure of the rate at which a substance decays. It is specific to each substance and can be found in a decay rate table or calculated using experimental data.

How do I convert grams to moles?

To convert grams to moles, you need to know the molar mass of the substance. You can find this by adding the atomic masses of each element in the substance. Then, use the formula moles = mass / molar mass to calculate the number of moles.

Can half-life be used to predict future decay?

Yes, half-life can be used to predict future decay. The half-life of a substance is constant, so if you know the initial amount of the substance and its half-life, you can calculate the amount remaining after a certain amount of time has passed.

How do I calculate the amount of a substance remaining after a certain number of half-lives?

The formula for calculating the amount of a substance remaining after a certain number of half-lives is: At = A0(1/2)n, where At is the amount remaining after n half-lives, A0 is the initial amount, and n is the number of half-lives that have passed.

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