B.) Mass Defect & Binding Energy for Astatine 21885At

In summary, the conversation discusses the process of obtaining the mass defect, binding energy, and binding energy per nucleon for astatine 218 (atomic mass = 218.008684 u). There is a discrepancy in the results due to a mistake in calculation or data entry. The conversation also mentions the use of units and conversion factors in the calculations.
  • #1
StudentofPhysics
67
0
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?
 
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  • #2
I think you have to include the electrons.
The numbers are easier if you keep it all in MeV instead of kg.
 
  • #3
mass defect takes place in the nucleus though
 
  • #4
You do include the electrons..

mass defect = (z*massproton+n*massneutron)-(matom-z*masselectron)
 
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  • #5
use units..

binding energy = massdefect*C^2

1 unit is approx = 931,494 MeV use that its easier
 
  • #6
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)
 
  • #7
ok i'll try that but my book says nothing about including electrons
 
  • #8
ok its right thanks

no idea why my book left that out..money well spent
 
  • #9
you should study in Denmark.. we get the books for free.. until University (college?)
 
  • #10
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
 
  • #11
As do we in America, I'm in college.
 
  • #12
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
 
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  • #13
thats what I did...
hmmmwould you mind running it quickly and seeing if you get a number other than 34.8 MeV?
 
  • #14
the correct answer in u was 1.810725 u for the mass defect
 
  • #15
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
 
  • #16
If i do like this i get:

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

don't know if that's the correct answer :S
 
  • #17
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.,. got to be right
 
  • #18
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
 
  • #19
ok its correct, I'm going back through it all to see what we did differently.
 
  • #20
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
 
  • #21
yea that's what happened I guess or I must've entered it wrong in my calculator some how...

anyway, much appreciation for the help.
 
  • #22
Always a pleasure to help (other) students.. :) even though I'm just in high school
 

1. What is mass defect?

Mass defect is the difference between the mass of an atom and the sum of the masses of its individual protons, neutrons, and electrons. This difference is due to the conversion of some mass into energy during nuclear reactions.

2. How is mass defect related to binding energy?

Mass defect is directly related to binding energy. The greater the mass defect, the higher the binding energy of the nucleus. This means that the nucleus is more stable and requires more energy to break apart.

3. What is the significance of studying mass defect and binding energy?

Studying mass defect and binding energy helps us understand the stability and behavior of atomic nuclei. It also allows us to predict the energy released or required in nuclear reactions, which is important in fields such as nuclear energy and medicine.

4. How is Astatine 21885At related to mass defect and binding energy?

Astatine 21885At is a radioactive isotope of astatine with a mass defect and binding energy that can be calculated using the mass of its constituent particles. The study of this isotope can provide valuable insights into the properties of astatine and nuclear reactions involving this element.

5. Can mass defect and binding energy be measured experimentally?

Yes, mass defect and binding energy can be measured experimentally using techniques such as mass spectrometry and nuclear reactions. These measurements can provide valuable data for further research and validation of theoretical models.

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