Transcript Aim: How can we explain Einstein’s energy

Aim: How can we explain
Einstein’s energy-mass
relationship?
Do Now:
In the nucleus of any atom, there exists protons
that are tightly packed together. How come they do
not repel each other as any other positively
charged objects would when brought close to one
another?
Strong Nuclear Force
• Very strong (the strongest of
the four forces)
• Short ranged
• Holds protons and neutrons
(nucleons) in the nucleus
together
Atomic Mass Unit (u)
• Also referred to as universal mass
unit
• 1/12 of a
atom
• 1 u = 1.66 x 10-27 kg
What is the atomic mass of Carbon-12?
= 12(1.66 x 10-27 kg)
= 1.99 x 10-26 kg
Energy-Mass Relationship
• Energy and mass are
equivalent
2
E = mc
• Units: Joules or eV
• 1 u = 9.31 x 102 MeV
• 1 MeV = 106 eV
•If mass is in kg, it converts to
energy in J through the formula
E = mc2
•If mass is in u, it coverts to
energy in MeV through the
conversion
1 u = 9.31 x 102 MeV
What is the energy equivalent of
the rest mass of a proton?
Rest mass of a proton = 1.67 x 10-27 kg
E = mc2
E = (1.67x10-27 kg)(3.00 x 108 m/s)2
E = 1.5 x 10-10 Joules
What is the energy equivalent of
a 60 kg boy?
2
mc
E=
8
2
E = (60 kg) (3.00 x 10 m/s)
E = 5.4 x 1018 Joules
Mass Defect
•The difference in the
mass of an atomic
nucleus and its
individual nucleons
Mass of proton = 1.0073 u
Mass of neutron = 1.0087 u
Find the mass of
2 protons = 2(1.0073 u)
+ 2 neutrons = 2(1.0087 u)
4.0320 u
The actual mass of
is 4.0016 u
What is the mass defect?
4.0320 u
- 4.0016 u
0.0304 u
Convert this mass defect to energy
So why did some of the mass turn into energy?
Binding Energy
• Energy needed to bind
nucleus together
• This is the energy that goes
into the strong nuclear force
Mass Defect = Binding Energy
This is part of Einstein’s Theory of
Special Relativity
Albert Einstein
1879-1955
If a deuterium nucleus has a mass
of 1.53 x 10-3 u less than its
components, this mass represents
an energy of
1.53 x 10-3 u x 9.31 x 102 MeV
1u
= 1.42 MeV
When an electron and its antiparticle
(positron) combine, they annihilate
each other and become energy in the
form of gamma rays.
The positron has the same mass
as the electron. Calculate how
many joules of energy are
released when they annihilate.
m = mass of electron plus positron
= 2 x (9.11x 10-31 kg)
E = mc2
E = 2(9.11x10-31kg)(3.00x108m/s)2
E = 1.64 x 10-13 J
What conservation law prevents this
from happening with two electrons?
The law of conservation of charge:
charges must be the same on both
sides of the equation
electron (-1e) + positron (+1e) =
gamma rays (energy, charge of 0)
electron (-1e) + electron (-1e) ≠ 0