Physics - Radioactivity - Mass defect/ Binding Energy

Thanks in advance!
Q2aii) I'm always getting an answer slightly different to the mark scheme and I can't figure out why.
e.g. 4.00260, but i got 4.0319
Can anyone kind enough, give me a detailed calculation of how to get to the numbers explained in the Mark Scheme?

Question:
https://pmt.physicsandmathstutor.com/download/Physics/A-level/Topic-Qs/AQA/08-Nuclear/Set-A/Radioactivity.pdf

Mark Scheme:https://pmt.physicsandmathstutor.com/download/Physics/A-level/Topic-Qs/AQA/08-Nuclear/Set-A/Radioactivity%20MS.pdf

Sounds like an error with the constants used. I don't know the masses involved (no constants sheet, sorry) but as long as you do the equation the way it's shown in the notes, i.e. the mass of U283 - alpha - whatever_has_90_protons_(234-90)_neutrons and use mass-energy equivalence to find the energy, you'll be fine.

What did you do to get 4.0319

Proton rest mass = 1.00728u or 1.673x10^-27 Kg
Neutron rest mass = 1.00867u or 1.675x10^-27 Kg
Electron rest mass = 5.5x10^-4u or 9.11x10^-31 Kg
Atomic Mass Unit = 1.661x10^-27 Kg
(1u = 931.5MeV)


(2x1.00728) + (2x1.00867) = 4.0319

Also, Where did 238.05076 and 234.04357 come from? - Is that meant to be the relative atomic mass of Uranium and Thorium, if so why didn't they just use 238 and 234?

Many Thanks to you guys who are helping!

how do you find out proton rest mass in atomic units? I'v used my AQA data sheet and done: 938.257/931.5= 1.007253892u .... How did you do it to get your answer of 1.00728u

It's on the AQA data sheet, right under proton rest mass. - 1.00728u
And where did you get 938.257 from?

2nd page of data sheet... the rest energy of a proton in the top left table is 938.237MeV, but you're method is better because i see it more in markschemes. thanks!

I see it, so how come it gives us it wrong on the first page and which should we use in the exam? Yours or the sheets?
I've got my actual exam this friday, so decisions to make...

use your method because i see that in markschemes.

Thanks in advance!
Q2aii) I'm always getting an answer slightly different to the mark scheme and I can't figure out why.
e.g. 4.00260, but i got 4.0319
Can anyone kind enough, give me a detailed calculation of how to get to the numbers explained in the Mark Scheme?

Question:
https://pmt.physicsandmathstutor.com/download/Physics/A-level/Topic-Qs/AQA/08-Nuclear/Set-A/Radioactivity.pdf

Mark Scheme:https://pmt.physicsandmathstutor.com/download/Physics/A-level/Topic-Qs/AQA/08-Nuclear/Set-A/Radioactivity%20MS.pdf

Proton rest mass = 1.00728u or 1.673x10^-27 Kg
Neutron rest mass = 1.00867u or 1.675x10^-27 Kg
Electron rest mass = 5.5x10^-4u or 9.11x10^-31 Kg
Atomic Mass Unit = 1.661x10^-27 Kg
(1u = 931.5MeV)


(2x1.00728) + (2x1.00867) = 4.0319

Also, Where did 238.05076 and 234.04357 come from? - Is that meant to be the relative atomic mass of Uranium and Thorium, if so why didn't they just use 238 and 234?

Many Thanks to you guys who are helping!

The nuclear mass of alpha particle SHOULD NOT or CANNOT be computed from the sum of the mass of the constituent particles in the alpha particle. (Why? Study the binding energy definition)

4.00260 is the atomic mass of He-4 atom NOT the nuclear mass of alpha particle because its nuclear mass is 4.001506u.

For such questions, the nuclear mass of the particles involved in the nuclear reaction is usually given or can be found in some datasheet. I believe the original question that you quoted would give the nuclear mass or the atomic mass of the nuclear nuclides within the question.

Both 238.05076 and 234.04357 could be nuclear mass or atomic mass of the U-238 and Th-234, respectively.

For a nuclear reaction, mass numbers are seldom used to compute the mass defect.

Binding energy - amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system.
I'm not how this states why you can't work out the nuclear mass of an alpha particle from the sum of the mass of the constituent particles
....

.....
Why a He-4 atom and not an alpha particle??
...

.....
238
92 U , was given in the question, if that's what you mean...
...

How do you translate the binding energy definition to a equation using conservation of mass-energy law? Check your textbook.

Hi,

I've read the guidelines and now know how to post my questions properly, thanks!

E=mc^2 .

So you times the Mass of the 2 protons and 2 neutrons by speed of light squared.

I know you can't just give me the answer, but I don't see how this states you can't use it for an alpha particle, going to need another clue

Binding energy/mass defect is the energy to separate/join nucleons. Alpha particle is made of nucleons, so i don't see why you cant do it for this....

Many Thanks for the Guidelines and your help!!

It seems that there is a gap in your knowledge of nuclear physics. See the following website.

https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/10%3A__Nuclear_Physics/10.03%3A_Nuclear_Binding_Energy

So the bit I am missing is that is that the alpha particle is made of Protons and Neutrons, but is not a nucleus in itself, it hasn't got electrons surrounding it, therefore it can't have a binding energy, because the binding energy is the energy to separate a nucleus.

Okay, so for a 4-He, you do (2x1.00728)+(2x1.00867) - (2x5.5x10^-4) = 4.0308, which still doesn't give me 4.00260 though,
- in the question it only gives you the atomic mass and the atomic number of uranium and not the helium nucleus.

So where am I going wrong now??

It seems that you are missing more than the bit or maybe due to exam stress or not reading thing properly.

The answer is already on the website.

Figure 10.3.1 should have answered your doubt. IMO, it clearly illustrates the concept of binding energy or mass defect.

Alpha particle is a bounded system with only protons and neutrons NOT separated protons and neutrons.

If you want to calculate the mass of alpha particle you need to know the mass defect and equation 10.3.1 in the website tells you so.


As I have already mentioned, the original question would give you either atomic mass or nuclear mass of the nuclides involved in the nuclear reaction.

What you quoted is NOT the whole of the original question.

You are NOT required to calculate the nuclear mass unless the question asks you to compute the nuclear mass, you are required to use the nuclear mass.

oooooooooooh, I Understand now, how did i miss that, well, my exam is on this thursday, so i'm trying my best not to let the stress get on top of me.

The whole question:

It doesn't give you anything to do with the 4-He in the WHOLE question.

Sorry if i am being a bit of a pain, but I still don't know how they got the 4.00260
Is it too much to ask for a worked example, labelled/explained?