Calculating the Decay Constant of Carbon 14

[EIRE2003]

Carbon14 has a half life of 5730 yrs. This is the only information i am given.

Caluculate the decay constant of Carbon 14.

This is what I have done.

dN/dt = -lambda(N)

I know the Avogadro Constant is equal to 6x10^23

So i am using 1kg in my formula.

14C = 6 x 10^23 x 1000/14

where do i go from here??

 

[Doc Al]

Half life and decay constant are just two ways of expressing the rate of radioactive decay. Half life (T) uses a base of 2:
$$X = X_0 2^{-\frac{t}{T_{half}}}$$

Decay constant (λ) uses a base of "e":
$$X = X_0 e^{-\lambda t}$$

You can convert from one to the other. Hint: $$2 = e^?$$

 

[EIRE2003]

ok i used dN/dt

which is 0.693 x 6 x 10^23/5730x 360 x 24 x 3600 x 14
which is equal to 3 x 10^28 s^-1

Is that right??

 

[jcsd]

Remeber that 1/λ is going to be equal to the mean lifetime of a C-14 particle, your figure gives a mean lifetime of about 3 x 10^-29 seconds, the mean lifetime is always longer than the half-life so the anbswer MUST be wrong.

Use Dr. Al's hints.

 

[Doc Al]

Avogadro's number is irrelevant.
$$2 = e^{0.693}$$
so... $\lambda = \frac{0.693}{T_{half}}$

 

[EIRE2003]

Ah i don't understand it.
Im looking at an example in a book and it has the second formula he gives,

ie N=No e^-lambda t

therefore dN/dt=-No Lambda e ^-lambda t = - lambda N

When N =12, dN/dt = -lambda 10^12

Now lambda = 0.693 / T1/2

 

[Doc Al]

decay rate vs. decay constant?

Perhaps you are confusing decay rate (which is dN/dt) with decay constant (which is λ)?