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

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 (1879 - 1955)

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) 50 % of the speed of light b) 99.9% of the speed of light

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 ( 1 - 0.52c2 /c2 ) ½ L = 1.5 ( 1 - 0.25 ) ½ L = 1.3 m b) L = Lo ( 1- v2/c2)1/2 L = 1.5 ( 1 - 0.992c2 /c2 ) ½ L = 1.5 ( 1 - 0.98 ) ½ L = 0.21m or 21 cm

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) 50 % of the speed of light b) 99.9% of the speed of light T = To / ( 1- v2/c2)1/2 T = 5 / ( 1 - 0.52c2 /c2 ) ½ T = 5 / ( 1 - 0.25 ) ½ T = 5 / 0.866 T = 5.77 years Age difference = 0.77 y ( 9 months) T = To / ( 1- v2/c2)1/2 T = 5 / ( 1 - 0.992c2 /c2 ) ½ T = 5 / ( 1 - 0.98 ) ½ T = 5 / 0.141 T = 35 years Age difference = 30 y

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?

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 10 -13 kg 25 x 30 x 60 = ( 3 x 10 8 ) 2

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

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

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.

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.

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 x10-19 C 0 = 8.9 x10 -12 Fm- 1

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 3 - 4 fm So the energy needed to remove a nucleon from the nucleus, WD = F x d = 200N x 3.5 fm = 700 x 10 -15 J = 4MeV. ( / by 1.6 x 10-13 J to get Mev)

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