Mass Defect Problem

[StudentofPhysics]

1. For astatine 21885At (atomic mass = 218.008684 u) obtain each of the following:

(a) The mass defect in atomic mass units
wrong check mark u
(b) the binding energy (in MeV)
MeV
(c) the binding energy per nucleon (in MeV)
MeV





2. Shown in atempt



3. ok, I don't see how I'm wrong here:

A.)

218 - 85 = 133 = # of neutrons
85(1.6726 x 10^-27 Kg) + 133(1.6749 x 10^-27 Kg) = 3.649327 x 10^-25 Kg

(3.649327 x 10^-25 Kg) / (1.6605 x 10^-27 Kg) = 219.772779 u

219.772779 u -218.008684 u = 1.764095 u.

This is not correct. What am I doing wrong?

[Meir Achuz]

I think you have to include the electrons.
The numbers are easier if you keep it all in MeV instead of kg.

[StudentofPhysics]

mass defect takes place in the nucleus though

[Maxwells Demon]

You do include the electrons..

mass defect = (z*massproton+n*massneutron)-(matom-z*masselectron)

[Maxwells Demon]

use units..

binding energy = massdefect*C^2

1 unit is approx = 931,494 MeV use that its easier

[Maxwells Demon]

but remember to use the right atom weight not the one in the periodic table, cause its an average of the percentage of the isotopes in nature (or something like that)

[StudentofPhysics]

ok i'll try that but my book says nothing about including electrons

[StudentofPhysics]

ok its right thanks

no idea why my book left that out..money well spent

[Maxwells Demon]

you should study in Denmark.. we get the books for free.. until University (college?)

[StudentofPhysics]

ok I'm getting it equals 34.8 MeV and this isn't right
what am I doing wrong here.

Again, my book shows how to convert from kg in J then into eV then into MeV.


And I had to use u because that was the required unit in the first part of the problem

[StudentofPhysics]

As do we in America, I'm in college.

[Maxwells Demon]

all right.. the first result was in units and correct right?

take it and and make it into kg by: 1 u = 1,6605655*10^-27kg

and then make it into joule by: x kg * (3*10^8)^2 this is just c squared

and make the joule into eV by: 1eV = 1,602189*10^-19 J

and of course into MeV by mega means 10^6

[StudentofPhysics]

thats what I did....
hmmm


would you mind running it quickly and seeing if you get a number other than 34.8 MeV?

[StudentofPhysics]

the correct answer in u was 1.810725 u for the mass defect

[StudentofPhysics]

i did the following:
1.810725 u x 1.6605 x 10^-27 Kg = 3.00671 x 10^-27 Kg

3.00671 x 10^-27 Kg x (c^2) = 5.5715 x 10^-12 J

5.5715 x 10^-12 J / 1.6 x 10^-19 J = 34821826.4 eV = 34.82 MeV

[Maxwells Demon]

If i do like this i get:

1.810725 u * 931,494 MeV/u = 1686,68 MeV

don't know if thats the correct answer :S

[Maxwells Demon]

i also get this

1.810725 u x 1.6605 x 10^-27 Kg = 3.00671 x 10^-27 Kg

but then i get 2,70614*10^-10 J

and then of course: 1,68903 *10^9 eV = 1689,03

almost the same as the other result, but used more decimals with this one.,. gotta be right

[Maxwells Demon]

I'll write it with all the decimals:

1,810725*1,6695655*10^-27 = 3,00683*10^-27 kg

3,0068274649875*10^-27*(3*10^8)^2 = 2,70614*10^-10 J

(2,7061447184888*10^-10)/(1,602189*10^-19) = 1,68903*10^9 eV = 1689,03 Mev

[StudentofPhysics]

ok its correct, I'm going back through it all to see what we did differently.

[StudentofPhysics]

hmm, rerunning it i get the 2.7 x 10^-7 Joules too, not sure how i got the other number the first time.... maybe I wrote it down wrong

[StudentofPhysics]

yea thats what happened I guess or I must've entered it wrong in my calculator some how...

anyway, much appreciation for the help.

[Maxwells Demon]

Always a pleasure to help (other) students.. :) even though I'm just in high school