Taking Apart an Alpha Particle

[conniechiwa]

Homework Statement

An alpha (α) particle is the nucleus of a 4He atom and consists of 2 neutrons and two protons bound together. Let's take apart an α particle, step by step, looking at the energy required at each step. To do so, we may want to use the following atomic masses:
4He: 4.0026 u
3H: 3.01605 u
2H: 2.0141 u
2H: 1.00783 u
p: 1.00728 u
e: 0.000548 u
n: 1.00867 u

a) What is the energy required to remove the first proton?

Homework Equations

m=mf-mi
E=mcsquared

The Attempt at a Solution

mi=4.0026 u
mf=3.01605 u + 1.00728 u
mf=4.02333 u

m=mf-mi
m=4.02333 u - 4.0026 u
m=0.02073 u

E=mcsquared
E=(0.02073 u)((931.5 Mev/csquared)/u)(csquared)
E=19.309995 Mev

Did I use the right masses?

 

[Redbelly98]

Looks right to me. Just watch the number of sig figs in the final answer.

 

[conniechiwa]

It still doesn't accept my answer. =/

 

[Redbelly98]

That's weird. I didn't check your math in detail, just that the mass values seem right to me.

And you tried less precise numbers, eg. 19.3 or 19.31 MeV?

 

[conniechiwa]

For some reason the correct answer was 19.8 Mev, but that doesn't make sense to me. >_<

 

[Redbelly98]

Hmmm, the 0.5 MeV difference happens to be 1 electron mass, but I'm not seeing how to account for that.

 

[alphysicist]

I believe the masses for 4He, 3H, 2H, and H that are given in the original post are not the nuclear masses, they are the masses for neutral atoms.

You can see that the mass for H (it's mislabeled as 2H) is not equal to the mass of a proton, but is the mass of a proton and electron.

So the nuclear masses must first be found from the atomic masses given.

 

[conniechiwa]

I got the right answer for removing the first neutron using this method. Is this the right way to solve the problem? Maybe the problem is glitched. There was a crash in the system before the course started so there's still lots of glitches.

 

[alphysicist]

conniechiwa,

I got the right answer for removing the first neutron using this method. Is this the right way to solve the problem? Maybe the problem is glitched. There was a crash in the system before the course started so there's still lots of glitches.

Which method are you referring to? In my post I was talking about your work for part a: removing a proton from 4He.

Your method in your original post was okay except for one part: you were using the wrong masses. For example, you had that the initial mass was 4.0026u, but that is not correct. The mass of the 4He atom, including 2 electrons, is 4.0026u. But they want you to start with a 4He nucleus, so you must subtract the mass of the two electrons.

Similarly when you were finding the final mass. You used 3.01605u, but that is for a 3H atom, which includes 1 electron.

In other words, your total initial mass was too great by two electrons, and your total final mass was too great by one electron, so your final answer was off by a total of the (approximate) rest mass energy of one electron.


(In your last post your refer to removing a neutron; are you talking about going from 3H to 2H? If so, do you see why using the atomic masses given instead of the nuclear masses would not make a (noticeable) difference in that case?)

 

[conniechiwa]

Oh okay I think I understand. So if I were to do the steps for removing the first neutron, would I subtract 1 electron from 3H and then add 1 neutron to 2H?

 

[alphysicist]

Oh okay I think I understand. So if I were to do the steps for removing the first neutron, would I subtract 1 electron from 3H and then add 1 neutron to 2H?

If you are talking about going from 3H to 2H, then don't forget to subtract the electron from the 2H also. Since both the 2H atom and the 3H atom have one electron, your original method worked for the neutron removal because both sides were off by the same amount.

 

[Redbelly98]

I believe the masses for 4He, 3H, 2H, and H that are given in the original post are not the nuclear masses, they are the masses for neutral atoms.

You can see that the mass for H (it's mislabeled as 2H) is not equal to the mass of a proton, but is the mass of a proton and electron.

You're right, I did not read it carefully and thought they were nuclear masses. Since the relevant masses were the first two entries, I didn't bother to look farther down the list to notice H and p were different.

 

[LamyJamy]

How do you know how many electrons to subtract?

 

[alphysicist]

How do you know how many electrons to subtract?

The masses given in the original post are for neutral atoms. So the question to answer is how many electrons does a 4He atom need to have to be neutral? What about a 3H atom? and so on. By determining the number of protons and netrons that are in each type of nucleus, and thus the total charge of the nucleus, you can find the number of electrons that each neutral atom has.