4. Mass Defect

5. Outcomes
You will relate, qualitatively and quantitatively, the mass defect of the nucleus to the energy released in nuclear reactions, using Einstein’s concept of mass-energy equivalence

6. Nuclear Binding Energy
The energy required to separate the nucleons of a nucleus (can be equated to the strong forces holding the nucleus together)
Binding energy: the energy required to separate all of a nuclei’s protons and neutrons infinitely far apart
Binding energy = energy of (individual) nucleons – energy of nucleus
Eb = Enucleons - Enucleus

7. Mass Defect
The assembled nucleus is ALWAYS lighter than the parts that make it up
TWO WAYS TO THINKS OF THIS…
The energy added to the nucleus to separate the nucleons shows up as mass
Some of the mass of the nucleons is released as energy when they bind to make the nucleus

8. Einstein and Binding Energy
Einstein’s formula E=mc2 states that mass and energy are equivalent
Whenever the nucleus undergoes some change, mass converts into energy and the mass converted is known as the mass defect
Conservation of energy still applies: the energy of the individual nucleons is equal to the sum of the energy of the nucleus and binding energy, leading us to:
Eb = Enucleons – Enucleus

9. Calculations Mass Defect
mass defect = mass of the nucleons – mass of the assembled nucleus.
m = [N(1.6749x10-27) +Z(1.6726x10-27)] – (A)(u)
Where N = # of neutrons and Z = # of protons (predicted)
Where, A=atomic mass number (total number of nucleons) and u =1.66x10-27kg (actual)
Binding Energy
Energy = mass defect x speed of light squared
E=mc2

10. Sample Problem
The mass of a helium nucleus is x kg ( 4 2 He). What is the mass defect and binding energy of the helium nucleus? (Use the following for proton and neutron masses: proton = x kg and neutron = x kg)

11. Half-Life

12. Outcomes
You will perform simple, non-logarithmic half-life calculations

13. Radioactivity
The rate that a radioactive sample transmutes can be expressed by either its activity or its half-life
Half-life: is the time it takes one half of a radioactive sample to decay
Activity: the number of nuclei that change in a given period of time.
The standard SI unit for the activity is the Becquerel: 1Bq = 1decay/s

14. Graphing
What is the half-life of this particular material?

15. Half-life Calculations
THIS PART OF THE FORMULA IS NOT ON YOUR FORMULA SHEET!

16. Sample Problem
The half life of iodine-131 is days. What percentage of an iodine-131 sample will remain after days?

17. Homework Mass Defect and Half-life p. 182 #1-4
Calculation Questions: p. 817 #5 & 7 and p. 184 #1-5
Graph Question: p. 817 #8