Radioactive isotopes in use question help

I'm stuck on part C, can someone please help me?




The radioactive isotope of 131-Iodine is used for medical diagnosis of the kidneys. The isotope has a half life of 8 days. A sample of the isotope is to be given to a patient in a glass of water. The isotope is required to have an activity of 800kBq at the time it is given to the patient.


Calculate:


A) the activity of the sample 24 hours after it


B) the activity of the sample when it was prepared 24 hours before it was given to the patient


C) the mass of the 131-I in the sample when it was prepared


I got the right answer for part A and B but I'm stuck on C. I know that Mass=moles x molar mass and that 1 mole = Avogadro constant but when I tried to do (131 x 6.02x10^23) I'm way off

Activity A = λN

where N is the number you want in your equation.
You find λ from the half life and A is the activity when prepared if N is the number of active nuclei when prepared.

Oh okay, thanks for replying,
so I found N then multiplied it by the Avogardo constant to get 6.92x10^11 then I did 131/)6.92x10^11) which is 1.8927x10^-10 g is that right? Or did I make up a load of rubbish?

I can't really comment without seeing all your working and your answer to b)
1. you need to take the value for the activity from part b) because it's about the time of preparation
2. N = A/λ give the number of atoms of iodine. (Have you got the correct λ?)

3. Then this number divided by the Avogadro constant gives the number of moles of iodine.

4. This then gives the mass.

That's the method.

Yes that's the correct answer, however I suspect you meant to say that you divided it by Avogadro's constant? Number of moles = N/N_A​

The activity from part B is 872193Bq so 870 kBq

λ is ln2/(8x24x60x60) = 1.00x10^-6

So N is 8.9674x10^11

So N/the Avogadro constant =

8.9674x10^11 / 6.02x10^23 = 1.4448x10^-12

So mass is 131 x 1.4448x10^-12 = 1.89x10^-10 g = 1.9x10^-13kg

How do you get N is 8.9674x10^11

from N= A/λ

when A = 870kBq (so you say)
and λ = 1.00 x 10⁶

Surely that gives N = 8.7 x 10¹¹

The rest is correct.