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1) A=λN

2) A=A0exp^-(λt)If half-life increases, λ decreases, and A decreases according to 1); but,

If half life increases, λ decreases, hence exp^-(λt) decreases, A should decreases according to 2)Why is this so? Where went wrong? Thanks!

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- Thread starter Angela Liang
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In summary, there is confusion over the relationship between the two equations given. While the first equation suggests that A decreases as λ decreases, the second equation suggests that A increases as λ decreases. This is not correct as graphing the function e^(-x) shows that it actually increases as x decreases. The second equation may be incorrect and should possibly be N=N0e^(-λt) instead.

- #1

- 36

- 1

1) A=λN

2) A=A0exp^-(λt)If half-life increases, λ decreases, and A decreases according to 1); but,

If half life increases, λ decreases, hence exp^-(λt) decreases, A should decreases according to 2)Why is this so? Where went wrong? Thanks!

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Angela Liang said:If half life increases, λ decreases, hence exp^-(λt) decreases

This doesn't look correct. Given the function ##Y=e^{-x}##,

##Y## should increase if ##x## decreases since ##e^{-x}=\frac{1}{e^x}##. Graphing this equation should immediately show you how the function behaves.

Angela Liang said:1) A=λN

2) A=A0exp^-(λt)

Hmmm. I think the second equation should be ##N=N_0e^{-λt}##, where ##N## is the number of nuclides remaining after time ##t##.

See this page: https://www.miniphysics.com/activity-half-life-and-decay-constant.html

- #3

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Thanks!Drakkith said:This doesn't look correct. Given the function ##Y=e^{-x}##,

##Y## should increase if ##x## decreases since ##e^{-x}=\frac{1}{e^x}##. Graphing this equation should immediately show you how the function behaves.

Hmmm. I think the second equation should be ##N=N_0e^{-λt}##, where ##N## is the number of nuclides remaining after time ##t##.

See this page: https://www.miniphysics.com/activity-half-life-and-decay-constant.html

Activity is a measure of the rate at which a substance decays, or undergoes a chemical or nuclear transformation. It is usually expressed in units of disintegrations per unit time, such as becquerels or curies.

Half-life is the amount of time it takes for half of the atoms in a radioactive substance to decay. It is a characteristic property of each radioactive isotope and can range from fractions of a second to billions of years.

The relation between activity and half-life is that the activity of a radioactive substance decreases as its half-life increases. This means that the longer the half-life, the slower the rate of decay and the lower the activity of the substance.

Activity is calculated using the equation A = λN, where A is activity, λ is the decay constant, and N is the number of radioactive atoms present. Half-life is calculated using the equation t1/2 = ln(2)/λ, where t1/2 is half-life and λ is the decay constant.

The main factor that can affect the relation between activity and half-life is the type of radioactive substance. Different substances have different decay rates and therefore different half-lives. Other factors that can influence this relation include temperature, pressure, and the presence of other substances that may affect the rate of decay.

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