# Math Help - A Physics [Quantum Theory] Problem... help please...

1. ## A Physics [Quantum Theory] Problem... help please...

"An instable nucleus that was initially at rest decays into a nucleus of fermium-252 containing 100 protons and 152 neutrons and an alpha particle that has a kinetic energy of 8.42 MeV. The atomic masses of helium-4 and Fermium-252 are 4.00260 u and 252.0849 u"

I would like to know how to calculate
1. the atomic number of the original unstable nucleaus.
2. the Velocity of the alpha particle.
And could someone please explain to me breifly where does this KE of the alpha particle come from? I was a little bemused by that bit in my lesson.
And also, hypothetically, say the fermium-252 nucleus went through a decay which a Beta- particle was produced, how does this affect the atomic number of the nucleus? Please explain this to me. I was also confused by that.

Thanks.

2. Originally Posted by apple12
"An instable nucleus that was initially at rest decays into a nucleus of fermium-252 containing 100 protons and 152 neutrons and an alpha particle that has a kinetic energy of 8.42 MeV. The atomic masses of helium-4 and Fermium-252 are 4.00260 u and 252.0849 u"

I would like to know how to calculate
1. the atomic number of the original unstable nucleaus.
2. the Velocity of the alpha particle.
And could someone please explain to me breifly where does this KE of the alpha particle come from? I was a little bemused by that bit in my lesson.
And also, hypothetically, say the fermium-252 nucleus went through a decay which a Beta- particle was produced, how does this affect the atomic number of the nucleus? Please explain this to me. I was also confused by that.

Thanks.
I suppose topsquawk deserves a rest. Briefly:

$\alpha$-decay: $^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}\text{He}$. Therefore $A - 4 = 152 \Rightarrow A = 156$ and $Z - 2 = 100 \Rightarrow Z = 102$.

You're told the KE of the alpha particle. Convert this energy from MeV into J (that is, convert to SI units). Now use the formula (that you should know) that links KE and velocity and solve for v (the unit will be m/s) ....

There's a mass difference between the mass of the original nucleus and the masses of the helium-4 (the alpha particle) and Fermium-252. And you know $E = mc^2 \, ....$

$\beta$-decay: $^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + e^{-} + \nu$.

3. Originally Posted by apple12
And could someone please explain to me breifly where does this KE of the alpha particle come from? I was a little bemused by that bit in my lesson.
Some of the mass-energy coming from the decay is changed to momentum (and hence KE) during the decay, otherwise we woudn't see the decay products and know that a decay had occured. Remember that all of the mass-energy from the decay has to be used and that the daughter nucleus (the nucleus left over after the decay) is going to be basically stationary, so that leaves a relatively large amount of energy left over for the KE of the escaping particles.

-Dan