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need urgent help with physics (Radioactive H/Lives) watch

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1. I need help with the following questions:

1 If a sample of radioactive isotope has a half life of 2 years how much of the original sample will be left at the end of the second year?
After the third year?
After the fourth year?

2 A sample of a particular radioisotope is placed near a Geiger counter, which is observed to register 160 counts per minute. Four hours later the detector counts at a rate of 10 counts per minute. What is the half life of the material?

3 The isotope cesium-137, which has a half life of 30 years, is a product of nuclear power plants. How long will it take for this isotope to decay to about one eigth its original amount?

4 A certain radioactive substance has a half life of one hour. If you start with 25g of the material at noon, how much will be left at 3:00pm? How much at 6:00 pm? And how much at 10:00pm?
2. I am working on this now - will post solution here soon
3. 1 If a sample of radioactive isotope has a half life of 2 years how much of the original sample will be left at the end of the second year?

50%

After the third year?

35.4%

After the fourth year?

25%

2 A sample of a particular radioisotope is placed near a Geiger counter, which is observed to register 160 counts per minute. Four hours later the detector counts at a rate of 10 counts per minute. What is the half life of the material?

1 hour

3 The isotope cesium-137, which has a half life of 30 years, is a product of nuclear power plants. How long will it take for this isotope to decay to about one eigth its original amount?

After 30 years: 50%
After 60 years: 25%
After 90 years: 12.5% (one eighth)

4 A certain radioactive substance has a half life of one hour. If you start with 25g of the material at noon, how much will be left at 3:00pm? How much at 6:00 pm? And how much at 10:00pm?[/QUOTE]

12:00pm = 25g
1:00pm = 12.5g
2:00pm = 6.25g
3pm = 3.125g
4pm = 1.5626g
5pm = 0.78125g
6pm = 0.390625g
7pm = 0.1953125g
8pm = 0.09765626g
9pm = 0.048828125g
10pm = 0.024414062g

3pm = 3.125g
6pm = 391mg
10pm = 24.4mg

If you need working, I can provide in a few mins
4. (Original post by nessals02)
1 If a sample of radioactive isotope has a half life of 2 years how much of the original sample will be left at the end of the second year?
After the third year?
After the fourth year?
for these types of questions, you work out 0.5^(time / half-life)

e.g. after 2 years: 0.5^(2/2) = 0.5 i.e. 50%
after 3 years: 0.5^(3/2) = 0.354 i.e. 35.4%
after 4 years: 0.5^(4/2) = 0.25 i.e. 25%

(Original post by nessals02)
2 A sample of a particular radioisotope is placed near a Geiger counter, which is observed to register 160 counts per minute. Four hours later the detector counts at a rate of 10 counts per minute. What is the half life of the material?
for this, you work out log(activity at start / activity at end)/log(2)

e.g. log(160/10)/log(2) = 4

this gives you the amount of half-lives the sample decayed through, so if there are 4 half-lives in 4 hours, the half-life is one hour

(Original post by nessals02)
3 The isotope cesium-137, which has a half life of 30 years, is a product of nuclear power plants. How long will it take for this isotope to decay to about one eigth its original amount?
for this, you do -log(the amount at the end)/log(2)

e.g. -log(1/8)/log(2) = 3

this means the isotope has to go through 3 half lives, or 90 years.

(Original post by nessals02)
4 A certain radioactive substance has a half life of one hour. If you start with 25g of the material at noon, how much will be left at 3:00pm? How much at 6:00 pm? And how much at 10:00pm?
this is the same method as question 1.
5. As always, Elpaw provides great answers.

But remember that half-life is only a statistical probability. Something that is supposed to dacay a certain amount at after a certain time might just as well decay less or more (or not at all!). Good to write in the error analysis of a lab report

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