1. How would you describe these two properties?
Energy and mass
How would you describe these two properties?

2. Albert Einstein Famous for his theories of Relativity.
His ideas were far reaching
and counter-intuitive;
fast moving objects
appear shorter
travel slower through time
have more mass!
Albert Einstein
( )

6. Q1. Calculate the length of a 1.5m bike moving at;
50 % of the speed of light
99.9% of the speed of light
Q2. Calculate the age difference between twins if one of the
twins goes on a space adventure for 5 years by their clock
travelling at relativistic speeds:
a) % of the speed of light
b) % of the speed of light

7. Q1. Calculate the length of a 1.5m bike moving at;
50 % of the speed of light
99.9% of the speed of light a)
L = Lo ( 1- v2/c2)1/2
L = 1.5 ( c2 /c2 ) ½
L = 1.5 ( ) ½
L = 1.3 m b)
L = Lo ( 1- v2/c2)1/2
L = 1.5 ( c2 /c2 ) ½
L = 1.5 ( ) ½
L = 0.21m or 21 cm

8. Q2. Calculate the age difference between twins if one of the
twins goes on a space adventure for 5 years by their clock
travelling at relativistic speeds:
a) % of the speed of light
b) % of the speed of light
T = To / ( 1- v2/c2)1/2
T = / ( c2 /c2 ) ½
T = / ( ) ½
T = / 0.866
T = years
Age difference = 0.77 y ( 9 months)
T = To / ( 1- v2/c2)1/2
T = / ( c2 /c2 ) ½
T = / ( ) ½
T = /
T = years
Age difference = 30 y

9. Mass change in reactions
If a torch gives out light then:
its chemical energy
store decreases
its mass decreases.
How much mass does a 25W torch lose in 30 minutes of use?

10. Mass change in reactions
How much mass does a 25W torch lose in 30 minutes of use?
∆E = ∆mc2
∆E = ∆m c2
P∆t = ∆m c2
5 x kg
25 x 30 x =
( 3 x ) 2

11. Mass / Energy conversion during annihilation
Particle / antiparticle annihilation creates: two gamma photons each of energy mc2 (where m is the mass of the particle) and mass is converting to energy E = hf = mc2

12. Energy / Mass conversion during pair production
Remember that you are making TWO particles so you need double the energy in the gamma ray!

13. Energy conservation In Alpha decay there is a loss of mass
this energy is shared between the alpha particle and the recoiling daughter nucleus.
Beta decay is exactly the same and assume the mass of a Neutrino to be zero.

14. Electron Capture
An electron from an inner electron shell that is captured by the nucleus.
When this happens the energy that is created (from loss of mass) is carried away by a neutrino.
There is also an X-ray that is emitted due to the shell vacancy being filled by an electron from a shell further out.

15. Strong Nuclear Force 0 = 8.9 x10 -12 Fm- 1
The force of repulsion between two protons 1 x 10-15m apart is about N and must balance the strong force.
200
e = 1.6 x C
0 = 8.9 x Fm- 1

16. Strong Nuclear Force
The force of repulsion between two protons 1 x 10-15m apart is about N and must balance the strong force.
The strong force must become repulsive under 0.5 fm or the nucleus would collapse to a singularity!
The range of the strong force is about fm
So the energy needed to remove a nucleon from the nucleus, WD = F x d = 200N x 3.5 fm = 700 x J
= 4MeV. ( / by 1.6 x J to get Mev)

17. Summary
Einstein’s famous formula E=mc2 states that mass and energy are interchangeable
The large constant of proportionality means that a large amount of energy is equal to a small amount of mas
Nuclear interactions create large amounts of energy due to the strong force; this means that mass changes are not negligible
Annihilation and pair production convert energy to mass and vice-versa