[quangngaicity]

Hello everybody.

Information given:
Ra-226 decays by alpha decay into Ra-222
Energy of an alpha particle is 4.79 MeV
Suppose 1.00 grams of 226-Ra, freed of all its radioactive progeny, were placed in a calorimeter that contained 10.0 grams of water, initially at 25 degrees C.
Assume all alpha particle energy is thermalized, and neglect both the heat capacity of the calorimeter and heat loss to the surroundings. Calculate the temperature the water would reach after one hour.

Attempt at solution: It seems relatively simple; I'm using Q=mcdeltaT, but I'm unsure if I'm calculating Q right. First I took Avogadro's number and divided it by 226, to try and get the number of alpha particles that would be emitted if we let the sample decay entirely. Then, I took that number and divided by two, and set up a proportion with alpha particles/2 / half life = x/1 hour, x being the number of alpha particles emitted. Eventually I went on to get 26.7 degrees C- which seems really high to me. Can someone point me to the problem (if there even is one) in my process of calculating Q? (And I converted everything to the right units, of course, so it's not that)

Thank's a lot!

[Borek]

I got similar order of magnitude of ΔT (small, single degrees), but a different number.

I took that number and divided by two, and set up a proportion with alpha particles/2 / half life = x/1 hour, x being the number of alpha particles emitted.

Can you elaborate? And show the number of α particles emitted? Seems to me like your proportion assumes constant activity of the sample throughout the whole half life, that's definitely incorrect, and I don't get this division by 2.

[Enthalpy]

[...] I took Avogadro's number and divided it by 226

I doubt about that one too.

Half-life: the amount of ²²⁶Ra decays like e^-t/τ, and the half-life h is defined by e^-h/τ=0.5. Or you may prefer to compute the decay as 2^-t/h.

My general impression is that you're lagging behind the course, and that first re-reading the chapter about decay would take you less time than trying to solve this problem now.

[Borek]

[...] I took Avogadro's number and divided it by 226

I doubt about that one too.

Actually this part makes sense to me - there are 1 g /226 g/mol moles of Ra-226, so 1/226*N_A atoms, which is equivalent to N_A/226. That's the starting number of atoms, a reasonable thing to calculate.

[Enthalpy]

Oops. 

[Old_Doc48]

'Ra-226 decays by alpha decay into Ra-222' ...

Ck your decay product, I think your decay product should be Rn-222 not Ra-222. Alpha decay would drop your product atomic number to 86 = Radon