Half-Life Problem: Find Nuclei & Mass After 3 Hours

[joeshmo]

Homework Statement

Initially, a particular sample has a total mass of 200 grams and contains 256 x 1010 radioactive nuclei. These radioactive nuclei have a half life of 1 hour.

(a) After 3 hours, how many of these radioactive nuclei remain in the sample (that is, how many have not yet experienced a radioactive decay)? Note that you can do this problem without a calculator

(b) After that same amount of time has elapsed, what is the total mass of the sample, to the nearest gram?

Homework Equations

.5 ^(time/half life)
and then multiply that to initial amount



3. The Attempt at a Solution [/b
i got part A by dividing the initial amount by 8. I tried doing the same for part B but I keep getting it wrong

 

[daveb]

Think of it this way. When a sample decays, it loses a specific amount of energy. Since it's asking for the nearest gram, a quick thought experiment is to see how much energy per decay is required for 0.5 grams (convert 0.5 grams to MeV, then divide by the number of particles that decayed). How many MeV would eahcdecay have to be to lose that 0.5 grams (which would just barely not round down to 199 grams).

 

[truesearch]

Your answer to part (a) is OK but part (b) sounds like a 'trick' question to me.
Although you have found that only 1/8 of the atoms are still radioactive the other 7/8 of the atoms are still in the sample. If they emitted beta particles tis would not show as a change in mass on this scale (1g in 200g) If they emitted alpha particles then you have lost 7/8 of the original number of atoms worth of Helium, ie 224 x 10^10 helium atoms.
If I were you I would calculate this mass of helium and see if it is more than 1g. (i doubt it)
The decay mechanism is not mentioned !