Solving Radioactivity Problems - Half-Life, Decay Constant & More

[lando45]

Hey,

I am a little stuck with this question I have been set:

"A freshly prepared sample of a certain radioactive isotope has an activity of 9.0 mCi. After 4.00 h, its activity is 7.50 mCi.

(a) Find the decay constant.
(b) Find the half-life.
(c) How many atoms of the isotope were contained in the freshly prepared sample?
(d) What is the sample's activity 30.0 h after it is prepared?"

I have a bunch of radioactivity formulae, but I don't know which one to use, none of them really seem appropriate...

So could point me in the right direction as to how I go about solving these?

Many thanks,
Rory (Lando 45)

 

[imabug]

Hey,

I am a little stuck with this question I have been set:

"A freshly prepared sample of a certain radioactive isotope has an activity of 9.0 mCi. After 4.00 h, its activity is 7.50 mCi.

(a) Find the decay constant.
(b) Find the half-life.
(c) How many atoms of the isotope were contained in the freshly prepared sample?
(d) What is the sample's activity 30.0 h after it is prepared?"

I have a bunch of radioactivity formulae, but I don't know which one to use, none of them really seem appropriate...

So could point me in the right direction as to how I go about solving these?

Many thanks,
Rory (Lando 45)

Read the questions and jot down the variables it gives you (the 'givens') in one column. Read the question and write down what you're supposed to find in another column. Look at your equations and see which one uses all the givens that you have. start with that one.

 

[andrevdh]

The activity decreases exponentially with time $t$ according to
$$A=A_oe^{-\lambda t}$$
where $A_o$ is the activity at $t=o$ and $\lambda$ is the required decay constant.
The relation between the decay constant and the half-life $T_{\frac{1}{2}}$ is given by
$$\lambda T_{\frac{1}{2}} = \ln(2)$$

 

[lando45]

Hey, thanks for all your help, I've managed to work out parts a), b) and d), but I still have no clue as to how to calculate the answer to part c). The formula I have is:

Number of undecayed nuclei with time t: N = N0e^-decayconstant x time

 

[Hootenanny]

A useful formula to learn is;

$$A = \lambda N$$

-Hoot