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# Stuck on a radioactivity question watch

1. Polonium-212 decays into the stable isotope lead-208 by the emission of an alpha particle. Use the conservation of momentum to calculate the energy carried off by i) the alpha particle

Could somebody please give me an idea where to start. Thanks
2. Are you sure this is all the info?
3. (Original post by Bigchip)
Polonium-212 decays into the stable isotope lead-208 by the emission of an alpha particle. Use the conservation of momentum to calculate the energy carried off by i) the alpha particle

Could somebody please give me an idea where to start. Thanks
Assume the decaying Po is stationary. Its linear momentum is therefore zero. From conservation of momentum, momentum after decay must also be zero. That means the alpha and the recoiling Pb must go off in opposite directions (momentum is a vector quantity). You know the relative masses of the alpha (4) and the Pb (208) so you can get their relative velocities. Once you have the masses and relative velocities, you can get relative kinetic energies.

To get absolute energies, you would also need to know the total decay energy for this process

Quote this if you're still stuck
4. (Original post by Cora Lindsay)
Assume the decaying Po is stationary. Its linear momentum is therefore zero. From conservation of momentum, momentum after decay must also be zero. That means the alpha and the recoiling Pb must go off in opposite directions (momentum is a vector quantity). You know the relative masses of the alpha (4) and the Pb (208) so you can get their relative velocities. Once you have the masses and relative velocities, you can get relative kinetic energies.

To get absolute energies, you would also need to know the total decay energy for this process

Quote this if you're still stuck
Is the total decay energy the mass defect?
5. (Original post by Scaudwell)
Are you sure this is all the info?
I have also been given a table of exact masses of each nuclide and the question before wanted me to calculate the energy released in MeV in the reaction.
6. (Original post by Bigchip)
I have also been given a table of exact masses of each nuclide and the question before wanted me to calculate the energy released in MeV in the reaction.
Use the exact masses. Calculate mass change on decay (mass of alpha plus mass of Pb minus mass of Po). Energy equivalent of 1 amu is 931.5 MeV, hence can get energy change in MeV
7. (Original post by Cora Lindsay)
Use the exact masses. Calculate mass change on decay (mass of alpha plus mass of Pb minus mass of Po). Energy equivalent of 1 amu is 931.5 MeV, hence can get energy change in MeV
I have got the answer for that. What do i do with that answer? Your great help by the way. Thanks alot
8. (Original post by Bigchip)
I have got the answer for that. What do i do with that answer? Your great help by the way. Thanks alot
Ok. You know the relative energy of the alpha and the relative energy of the Pb. These added together are proprotional to the total decay energy (which you know), and you know the relative proportions associated with the alpha and the Pb

So you can write

for alpha

Alpha energy = Decay energy x (Proportion with alpha/(proportion with alpha + proportion with Pb))

and for Pb

Alpha energy = Decay energy x (Proportion with Pb/(proportion with alpha + proportion with Pb))

Ypu should find that almost all the energy is associated with the alpha

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