Nuclear physics - difference between Activity and Decay constant

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Zishi
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#1
Report Thread starter 9 years ago
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Hello,

I'm having difficulties in understanding the difference between Activity and the decay
constant. My Book gives definitions of these two things as follows:

"The probability that an individual nucleus will decay per unit time interval is known as the decay constant"

"The activity A of a radioactive sample is the rate at which nuclei decay or disintegrate"

The base units of both things are s-1. I guess these two are fairly the same things...if that's so, then why do we use them as separate things? :confused: Or if I'm wrong, then what's the difference between them?
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Stonebridge
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The activity of a sample (A) is the number of disintegrations per second. It's what you measure when you place a counter near the sample. The unit is Becquerel (Bq) but is actually just s-1. Number per second.
This activity depends on how much radioactive material you have in the sample. If you double the sample size (number of atoms) you will double the activity.
The decay constant lambda is the constant of proportionality between the activity of the sample (A) and the number of radioactive atoms (N) in the sample.
A = \lambda N

This means that, say, two samples of two different radioactive materials each with, for example, 1000 atoms each could have a different measured amount of activity.
The one with the larger decay constant would be the more radioactive sample even though there are the same number of atoms of both. This is because the one with the larger decay constant contains atoms which are "more likely" to disintegrate. Lambda also measures this "probability of decay".

If the value of lambda was 0.5 for one of the samples, then 0.5 x 1000 = 500
That sample would have an initial activity of 500 Bq

If the other sample had a lambda of 0.1, its initial activity would be 0.1 x 1000 = 100Bq

I say "initial" because as the atoms decay, the amount of radioactive substance gets less and the activity gets less. This gives the familiar exponential decay curve.
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Zishi
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Report Thread starter 9 years ago
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(Original post by Stonebridge)
The activity of a sample (A) is the number of disintegrations per second. It's what you measure when you place a counter near the sample. The unit is Becquerel (Bq) but is actually just s-1. Number per second.
This activity depends on how much radioactive material you have in the sample. If you double the sample size (number of atoms) you will double the activity.
The decay constant lambda is the constant of proportionality between the activity of the sample (A) and the number of radioactive atoms (N) in the sample.
A = \lambda N

This means that, say, two samples of two different radioactive materials each with, for example, 1000 atoms each could have a different measured amount of activity.
The one with the larger decay constant would be the more radioactive sample even though there are the same number of atoms of both. This is because the one with the larger decay constant contains atoms which are "more likely" to disintegrate. Lambda also measures this "probability of decay".

If the value of lambda was 0.5 for one of the samples, then 0.5 x 1000 = 500
That sample would have an initial activity of 500 Bq

If the other sample had a lambda of 0.1, its initial activity would be 0.1 x 1000 = 100Bq

I say "initial" because as the atoms decay, the amount of radioactive substance gets less and the activity gets less. This gives the familiar exponential decay curve.
Many thanks, got it! :yep:
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orapezit
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Clear and Useful. Good job.
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