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

E = mc2

• 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?

E = mc2

E = (60 kg) (3.00 x 108m/s)2

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 1 u

= 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