What is the correct solution for a nucleus with a diameter of 8x10^(-15)m?

[prolong199]

i have the following for a multiple choice question
.." If a nucleus had a diameter of 8x10^(-15)m what would its atomic mass be?..."

I have calculated the answer to be 512, however this is not a solution. The solutions are 7, 37, 64, 296. Is the correct solution here? Thanks

 

[Curious3141]

The neutron is "of the order" of 10^(-15) meters in diameter, and using that, I get the same answer as you (8^3 = 512).

The problem here is that order of estimates are not precise enough for this calculation. Particles ranging from 0.5*10^(-15) to 5*10^(-15) in diameter can legitimately be said to have an order of magnitude of 10^(-15) meters. Of course, using different actual values will give wildly different estimates.

So, I don't know. Unless you have an authoritative source for the diameter of a neutron, the question has no right answer. I would just go with the one that's closest to the calculation and hope for the best. I'd also complain about the question after the test.

 

[Andrew Mason]

i have the following for a multiple choice question
.." If a nucleus had a diameter of 8x10^(-15)m what would its atomic mass be?..."

I have calculated the answer to be 512, however this is not a solution. The solutions are 7, 37, 64, 296. Is the correct solution here? Thanks

Yes. Use proton radius = 1.2 fm.

AM

 

[Curious3141]

Yes. Use proton radius = 1.2 fm.

AM

Just for my own edification, where can you find reference values like these ?

 

[Curious3141]

Just as an illustration of how wildly other estimates can vary, http://hypertextbook.com/facts/1999/YelenaMeskina.shtml (various figures given, including a bad estimate of 2*10^(-14) m)

http://www.glafreniere.com/sa_protons.htm (10^(-15) m)

http://www.coral-lab.org/~marc/libro/insignificance_full.html (1.6*10^(-15) m)

Needless to say, each of these different values will give a different answer to the question. Which is why a question like this is bad unless one is given the diameter of a nucleon to be assumed when working out the question.

 

[Andrew Mason]

Just for my own edification, where can you find reference values like these ?

http://en.wikipedia.org/wiki/Atomic_nucleus#Nucleus_size" or "[URL
[/URL] are pretty good for finding just about anything, I find.

AM

 

[Curious3141]

http://en.wikipedia.org/wiki/Atomic_nucleus#Nucleus_size" or "[URL
[/URL] are pretty good for finding just about anything, I find.

AM

Thanks for the references, but my concern is that there are various other estimates out there. This sort of question is exquisitively sensitive to small variations in the assumed nucleon diameter.

 

[Andrew Mason]

Thanks for the references, but my concern is that there are various other estimates out there. This sort of question is exquisitively sensitive to small variations in the assumed nucleon diameter.

I think the diameter of a proton at 1.2 fm is determined by extrapolation from measurements of larger nucleii on the theory that the nucleus has uniform density. If you plot r against A^2/3 where r is the radius and A is the number of nucleons, you should get a line of slope r₀ = radius of proton/neutron.

AM

 

[Curious3141]

I think the diameter of a proton at 1.2 fm is determined by extrapolation from measurements of larger nucleii on the theory that the nucleus has uniform density. If you plot r against A^2/3 where r is the radius and A is the number of nucleons, you should get a line of slope r₀ = radius of proton/neutron.

AM

Ah, thanks for the clarification.