Alpha Decay of Polonium-210 Homework

[Lissajoux]

Homework Statement

Polonium isotope ${}_{84}^{210}Po$ is unstable and emits a 5.30MeV $\alpha$ particle.

i. Indentify the daughter nuclide (using a periodic table)

ii. Calculate the mass of the daughter nuclide.

Homework Equations

Mass of neutral ${}^{210}Po$ nuclide is 209.9829u

Mass of ${}^{4}He$ is 4.0026u

Note that taking the mass of the alpha particle as the mass of a neutral helium atom.

The Attempt at a Solution

i. [tex]{}_{84}^{210}Po \rightarrow {}_{82}^{206}? + {}_{2}^{4}\alpha + Q[/itex]

By looking at a periodic table, identified the daughter nuclide as: ${}_{82}^{206}Pb$

.. correct?

ii. Not sure how to do this. The mass of both sides of the equation must be the same I assume. Already know the mass of the alpha particle, it's the mass of the helium atom given. The mass of the neutral Po I assumed would refer to the nuclide after the alpha particle has been emitted, but this is Pb not Po.

Not sure how to get the values required to perform the calculation, which I guess would be:

[tex]M({}_{84}^{210}Po) - M({}_{2}^{4}\alpha) = M({}_{84}^{210}Pb)[/itex]

So 2 things with this part, how to I get the values of the masses? and is the equation to calculate the mass of the daughter nuclide correct?

Any help really will be appreciated.

 

[nickjer]

Your last equation is partially correct. You also need to subtract off the kinetic energy of the alpha particle.

 

[Lissajoux]

Is it correct to do this:

Mass of neutral ${}^{210}Po$ nuclide is 209.9829u

Mass of ${}^{4}He$ is 4.0026u

$$M({}_{84}^{210}Pb)=M({}_{84}^{210}Po) - M({}_{2}^{4}\alpha)=205.98u=0.19MeV$$

Not sure if it's that simple? If not, where am I going wrong?

 

[nickjer]

The masses were given to you. So those should be correct. Also it asks for the mass of Pb, so you should keep it in atomic units and not MeV. Also, as I said before, that is not correct. You still need to subtract off the kinetic energy of the alpha particle.

 

[Lissajoux]

How do I calculate the kinetic energy of the alpha particle in order to then subtract this?

 

[nickjer]

They give it to you already in the problem. (5.30MeV)

 

[Lissajoux]

Right, Ok.

So if I change the equation to this:

$$M({}_{84}^{210}Pb)=M({}_{84}^{210}Po) - M({}_{2}^{4}\alpha)-Q$$

Then I either take off that Q=5.30MeV from my answer then convert it from MeV to u, or convert 5.30MeV to u and then take it away from my answer given in u. If that makes sense.

 

[nickjer]

Do the latter part. Try to keep it in u's, so your final answer will be a mass and not energy.

 

[labview1958]

When Po is injested into the body. It emits alpha radiation. Does this radiation causes other materials in the body to become radioactive?