NUCLEAR MASS AND ENERGYPhysics 12

Clip of the day:

Minutephysics…on Einstein and uncertainty principle

http://www.youtube.com/watch?v=hSgIDgGpRpk

http://www.youtube.com/watch?v=7vc-Uvp3vwg&list=PL908547EAA7E4AE74

Protons, Neutrons and Electrons

The atom is composed of three subatomic particles:

A nucleon is a proton or neutron

Particle Charge(in C)

Symbol Mass(in kg)

Electron -1.602x10-19 e- 9.109 56x10-31

Proton 1.602x10-19 p+ 1.672 614x10-27

Neutron 0 n0 1.674 920x10-27

Atomic Nucleus

Atom described using: X – atomic symbol A – atomic mass

number (nucleon number)

Z – atomic number

Number of protons and electrons = Z

Number of neutrons = A - Z

XAZ

Strong Nuclear Force The electrostatic forces inside a nucleus would rip it apart

if there was not another force The strong force’s main job is to hold together the

subatomic particles of the nucleus By the end of the 1930’s physicists had determined that

nucleons attract each other This is the strongest force in the known universe which

works at very close range

Stability and the Nucleus:

Although the Strong Nuclear Force is strong enough to hold a small nucleus together, as the size of the nucleus becomes larger, the electrostatic forces (repulsion between protons) begin to become more important

As a result, if we consider various nuclei based on their Atomic Number and Neutron Number we get the following result:

Nuclides and Isotopes

Nuclides are different combinations of nucleons

Isotopes occur when an element (specific Atomic Number) has different numbers of neutrons (different Atomic Mass Numbers)

For example, there are three common isotopes of hydrogen:

Nuclear Binding Energy

The energy to separate all the nucleons in a nucleus is called the binding energy

Comparison: It takes 13.6eV to separate an electron

from a hydrogen atom However, it takes more than 20MeV to

separate a neutron from a helium-4 atom

Fusion and Fission

Fission is the splitting of an atom into two or more smaller ones

Fusion is the fusing of two or more smaller atoms into a larger one.

Mass Defect

Imagine if we were able to apply the 20MeV required to separate a neutron from helium-4, what would happen to it? Back to Einstein’s Special Theory of Relativity

and the fact that mass and energy are equivalent……

The mass of helium-4 (2p, 2n) is smaller than that of helium-3 (2p, 1n) and a neutron separately

The energy that was added to remove the neutron was converted into mass!

Mass defect = the difference between the mass of a nuclide and the sum of the masses of its constituents

Atomic Mass Unit (u) When dealing with nucleons, it is often more

useful to deal with mass in Atomic Mass Units (u) instead of kilograms as the masses are very small

Particle Mass(in kg)

Mass(in u)

Electron 9.109 56x10-31 0.000 549

Proton 1.672 614x10-27 1.007 276

Neutron 1.674 920x10-27 1.008 665

Example #1:

30

26

56

9206.55

N

ZAN

Z

A

umnucleus

Determine the binding energy in electron volts and joules for an iron-56 nucleus given that the nuclear mass is 55.9206u

eVxeVx 68

1079.856

10924.4

Then divide by the number of nucleons to get binding energy per nucleon:

7.88x10-11J x 1eV = = 4.924x108 eV 1.6x10-19J

Convert u to kg:0.5285u x 1.6605 x10-27kg = 8.77 x 10-11kg

JxE

smxxE

mcE

11

2827

2

10888.7

)/10998.2)(1077.8(

Try it

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