I Relativity

2. I Relativity • 1.Principle of relativity: All the laws of Physics are the same in all inertial frames • 2.The constancy of the speed of light: The speed of light in a vacuum has the same value, c=2.99792458 x108 m/s, in all inertial reference frames, regardless of the velocity of the observer or the velocity of the source emitting the light • In relativistic mechanics, there is no such thing as absolute length of absolute time. Events at different locations that are observed to occur simultaneously in one frame are not observed to be simultaneous in another frame moving uniformly past the first

3. Two events that are simultaneous in one reference frame are in general not simultaneous in a second frame moving relative to the first. Simultaneity depends on the state of motion to the observer, and is there not an absolute concept • Time Dilatation Δt=Δtp/ √(1- v2/c2) = γΔtp Where γ=1/ √(1- v2/c2) • The time interval Δt between two events measured by an observer moving with respect to a clock is longer that the time interval Δtp between the same two events measured by an observer at rest with respect to the clock. Δtp- proper time

4. A clock moving past an observer at speed v runs more slowly than an identical clock at rest with respect to the observer by a factor γ-1 • Proper time- the time interval between two events as measured by an observer who sees the events occur at the same position • Length Contraction • Proper length Lp of an object is the length of the object as measured by an observer at rest relative to the object • L=Lp / γ =Lp√(1- v2/c2) • Length contraction takes place only along the direction of motion

5. Relativistic energy • KE=γ mc2-mc2 • Er=mc2 –rest energy Total Energy =Kinetic Energy +Rest Energy • E =KE+mc2 =γmc2 • E=mc2 / √(1- v2/c2) • A stationary particle with ZERO kinetic energy has a energy proportional to its mass

6. Einstein’:s postulates of general relativity • 1.All the laws of nature have the same form for observers in any frame of reference, accelerated or not • 2. In the vicinity of any given point, a gravitational field is equivalent to an accelerated frame of reference without a gravitational field • General relativity also predicts extreme states of matter created by gravitational collapse. If the concentration of mass become very great, when a large star exhausts its nuclear fuel and collapses to a very small volume, a BLACK HOLE may form

7. II Quantum Physics • Electromagnetic radiation is emitted and absorbed by matter as though it existed in individual bundles called QUANTA • A quantum of electromagnetic energy is knows as a photons • Light behaves like a stream ofphotons, and this is illustrated by the photoelectric effect

8. When a piece of metal is illuminated by electromagnetic radiation (visible light, ultraviolet, or x-rays), the energy absorbed by electrons near the surface of the metal can liberate them from their bound state, and these electrons can fly off • The released electrons are knows as photoelectrons

9. Wave-only theory of light would predict three results: • A) There would be a significant time delay between the moment of illumination and the ejection of photoelectrons, as the electrons absorbed incident energy until their KE was sufficient to release them from the atom’s grip • B) Increasing the intensity of light would cause the electrons to leave the metal surface with greater KE • C) Photoelectrons would be emitted regardless of the frequency of the incident energy, as long as the intensity was high enough

10. None of these prediction was observed! • A) photoelectrons were ejected within few billionths of the second after illumination • B) Increasing the intensity of light did not cause photoelectrons to leave the metal surface with greater KE. More e- were ejected as the intensity was increased • C) If light of frequency lower than fo (threshold frequency) were used to illuminate the metal surface, no photoelectrons were ejected

11. Einstein postulated these observations by postulating that the energy of the incident electromagnetic wave was absorbed in individuals bundles (photons) • Energy of a photon is proportional to the frequency of a wave E=hf • h=6.63x10-34 J s– Planck constant • A certain amount of energy had to be imparted to the metal surface in order to liberate it – Φ – metal work function

12. Increasing the intensity of and the incident energy means bombardment with more photons and results in the ejection of more photoelectrons: KEmax=hf- Φ • E =hf –energy of each incident photon • Threshold frequency fo= Φ/h

13. The dual nature of light and matter: • Light has a dual nature, exhibiting both wave and particle characteristics

14. Because photons have wave and particle characteristic, perhaps all forms of matter have both properties • E=hf =hc/λ p=E/c =hc/cλ =h/λ – momentum of a photon • λ=h/p =h/mv – de Broglie wavelength of a particle • Frequency of matter waves: • f= E/h (Einstein relationship for photons)

15. III Atomic Physics • The Bohr Model Of The Atom • The light from a glowing gas, passed through a prism to disperse the beam into its components wavelengths, produces patterns of sharp lines called atomic spectra

16. the atomic spectra of all the elements:

17. The visible wavelength that appear in the emission spectrum of Hydrogen has been summarized by the Balmer Formula: • 1/λn=R(1/22-1/n2) • R-Ryderberg ct. = 1.1 x107 m-1 • Bohr’s postulated that the electron would orbit the nucleus only at certain discrete radii (when the e- is in one of these special orbits it does not radiate away energy) • If the e- absorbs a certain amount of energy, it is exited to a higher orbit, one with a greater radius

18. After a short time in this excited state, it returns to a lower orbit, emitting a photon in the process • Each allowed orbit-energy level, has a specific radius (corresponding energy), the photons emitted have only specific wavelengths • Bohr found that the energy of each state was a particular fraction of energy of the ground state • The energy of the n-th energy level: • En=(1/n2)E1 • E1- ground state energy= -13.6 eV

19. State energy is known as the ionization energy – the minimum energy that must be supplied to release the atom’s electron • En=(Z2/n2)(-13.6eV) • Z- nr of protons in the atom’s nucleus • When an exited electron drops from energy level n=j to a lower one n=I, the transition causes a photon of energy to be emitted, and the energy of the photon is the difference between the two energy levels: • E emitted photon =׀ΔE׀ = Ej –Ei • Wavelength of this photon: • λ=c/f =c/(Ephoton/h)=hc/ (Ej –Ei )

20. 1/λn=R(1/nf2-1/ni2)

21. Wave-Particle Duality • Electromagnetic radiation propagates like a wave but exchanges energy like a particle • A particle of mass m and speed v with linear momentum p=mv has an associated wavelength: de Broglie wavelength • λ=h/p • Bohr postulated that the electron’s orbital angular momentum, mevnrn, had to be an integral multiple of h=ħ/2π • mevnrn =nħ (ħ=h/2π), n=1,2,3 • 2 πrn=nh/ (mevn); 2rn=n (h/pe); 2πrn = n λe • The circumference of the e- ‘s orbit must equal to a whole number of wavelengths in order for it to be stable

22. IV Nuclear Physics • The nucleus of the atom of particles called protons and neutrons, which collectively called nucleons • Atomic nr. - Z –nr of protons • Neutron nr. (nr. of neutrons) - N • Mass nr. (nucleon nr.) – A =Z+N • Nuclei that contain the same nr. of protons but different nr. of neutrons are called izotopes

23. Strong nuclear force- binds neutrons and protons together • mp=1.6726x10-27kg= 1.00728 u • mn=1.6749x10-27kg= 1.00867 u • Atomic mass unit u defined as 1/12 the mass of 12C atom • 1u=1.6605x10-27kg • If we consider the deutron, the nucleus of deutrium an isotope of hydrogen that contains 1 proton and 1 neutron • mdeutron=2.01356 u • The difference between the mass of any bound nucleus and the sum of the masses, is called mass defect • Δm= (mp + mn)-md = 0.00239 u

24. The missing mass wasd converted to energy when the deutron was formed, is the enery needed to break the deutron into a separtate protonand neutron, and is called – the binding energy of the nucleus • Binding energy per nucleon (for deutron) • 2.23MeV/2 nucleons =1.12 MeV/nucleon

25. Nuclear Reactions • Ex:- NaturalRadioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom . -Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei), often producing free neutrons and photons (in the form of gamma rays). Fission of heavy elements is an exothermic reaction which can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments

26. - Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy. Large-scale thermonuclear fusion processes, involving many nuclei fusing at once, must occur in matter at very high densities and temperatures. • We write 11p ,11H, 10n, 00γ • Ex: 10n+19880 Hg→19779Au + ??X

27. Disintegration energy • Nuclear reaction must conserve total energy ΔE=(Δm)c2 • A general nuclear reaction: A+B→C+D+Q • Q- disintegration energy • Q<0- reaction is endothermic (endoergic) Q>- reaction is exothermic (exoergic) • Q=[(mA+mB)-(mC+mD)]c2 =Δmc2 • Most of energy is revealed as KE of the least massive product nuclei