Astronomy 101, Oct. 16, 2008 Announcements OWL Homework #3 now available. Due Sunday, 10/19, before midnight. No class next Tuesday. Final exam has been scheduled by the registrar. Date, time, and place: Monday, Dec. 15, 10:30 AM, Hasbrouck 20 Electrons can be in different orbits of certain energies, called energy levels. Atom Energy Levels Energy Different atoms have different energy levels, set by quantum physics. Atom 1: 92 protons, 143 neutrons, 92 electrons Atom 2: 92 protons, 143 neutrons, 91 electrons Atom 3: 91 protons, 143 neutrons, 91 electrons Atom 4: 92 protons, 144 neutrons, 92 electrons Which of these atoms are isotopes? 1. 2. 3. 4. 5. 1 and 2 2 and 3 3 and 1 1 and 4 3 and 4 A particular element always has the same number of protons atomic number = # protons atomic mass number = #protons + #neutrons (aka atomic weight ). Isotopes are the same element but with different atomic weights Bound electrons prefer to be in the lowest energy level, which is called the ground state. Electron cloud: Quantum means discrete! The electron energy levels are like a staircase... The electron can step from one level up or down to another level, but the bound electron cannot have an energy between levels nucleus Allowed energy levels for the bound electron Add just the right amount of energy, and the electron will jump to a higher energy excited state. If enough energy is given to the electron, it will be removed from the atom altogether resulting in an ION and a FREE ELECTRON. Unlike excitation, ionization does not require a discrete quantum amount of energy. The energy only needs to exceed some amount called the ionization potential which depends on the atom being ionized. 1
Atom energy levels are often depicted in a simple way as shown below. PRS Question! Atoms often spontaneously emit radiative energy (light). Which of the electron transitions shown below (A, B, C, D, or E) would cause the atom to emit light? Ionization. Energy added, not removed. 1. A 2. B 3. C 4. D 5. E 6. A and B 7. A and C 8. A, B, C not allowed 9. A, B, C, D 10. All of them Energy Excitation. Energy added, not removed. Increasing temperature (increasing microscopic kinetic energy) What happens to matter as its temperature increases? Phase transitions. Plasma: free electrons and free nuclei (many electrons stripped). Ionization: atoms broken apart (electrons stripped off atoms). Dissociation: molecules broken appart. Gas. (Can be molecules or atoms or both) Liquid. Solid. Opposite charges attract, but similar charges repel each other. The nucleus of helium contains two positive protons and two neutral neutrons. Why don t the similarly-charged protons in this nucleus push each other away? 1. There is a strong chemical bond inside the nucleus. 2. The attraction of the negatively-charged electrons holds the protons together. 3. There is a force that is even stronger than the charge force that holds the nucleus together, but it only acts on short distance scales, i.e., when particles are quite close together. Four fundamental forces of nature Electromagnetic force. Causes opposite charges to attract each other. Gravity. The strong nuclear force. Holds the nucleus together. The weak nuclear force. But what is a force? Most important forces in astronomy. Only effective on very small scales. Ah... time for Units 15 and 16 2
Units 15-16: Laws of Motion & Gravity Force and momentum Speed, velocity, and acceleration Mass vs. weight Newton s laws Conservation of momentum Angular momentum Speed, velocity, and acceleration speed rate at which an object moves, i.e. the distance traveled per unit time [m/s; mi/hr] velocity an object s speed in a certain direction, e.g. 10 m/s moving east acceleration a change in an object s velocity, i.e. a change in either speed or direction is an acceleration [m/s 2 ] Speed is an example of a scalar, a quantity that has a magnitude but no direction. Velocity and acceleration are vectors, the direction and magnitude are both important. Which of the following is least likely to be accelerating? velocity = acceleration x time Velocity and acceleration are both vectors, but time is a scalar quantity. 1. A car driving down a winding, narrow mountain road. 2. A racecar driver. 3. A car driving through Texas on the interstate. 4. A bumper car at a county fair. 5. A planet orbiting a star. 3
Force produces acceleration force = mass x acceleration acceleration = force mass Momentum An object s momentum (P) is simply its mass times its velocity. momentum = mass x velocity P = m v Velocity is a vector, so momentum is a vector too. The direction is very important! Force = ma Force is anything that can cause a change in momentum. If mass doesn t change, then a force must cause velocity to change, i.e., an acceleration. Momentum is Conserved P = m v P 1 = m 1 v 1 P 2 = m 2 v 2 If two objects collide and stick together, the final momentum must be the same as the initial momentum. P final = P 1 + P 2 This is why you want your linebackers to be huge! 4
Before: Momentum example 1: equal mass pool balls v 1 v 2 = 0 Object 1 has m 1 & v 1, so P 1 = m 1 v 1 Object 2 has m 2 & v 2 = 0, so P 2 = m 2 0 = 0 Total momentum: P total = P 1 + P 2 = m 1 v 1 After: v 1 = 0 Momentum must be conserved! P total (before) = P total (after) Momentum is transferred to ball 2 Ball 1 stops. Ball 2 moves away with v = v 1 v 2 Momentum example 2: equal mass balls moving in opposite directions at the same speed Before: After: v 1 v 2 v 1 v 2 Momentum must be conserved! P total (before) = P total (after) P total (before) = m 1 v 1 - m 2 v 2 = mv - mv = 0 Before: Momentum example 2: equal mass STICKY balls moving in opposite directions at the same speed v 1 v 2 Mass vs. Weight mass the amount of matter in an object weight the net force that a body exerts in the downward direction After: v 1 = 0 v 2 = 0 Momentum must be conserved! P total (before) = P total (after) P total (before) = m 1 v 1 - m 2 v 2 = mv - mv = 0 When in free-fall, in a sense you are weightless. 5
Sir Isaac Newton (1642-1727) Studied optics and nature of light Invented the reflecting telescope Invented calculus Connected gravity and planetary forces Philosophiae naturalis principia mathematica (published 1687) Laws of motion and gravity - certainly changed the world!! Newton: the laws of physics should be the same everywhere... Newton s Laws of Motion 1 Without a force acting on it, an object moves with constant velocity. Put another way: 1 Objects in motion tend to remain in motion, and objects at rest tend to remain at rest. Newton s Laws of Motion acceleration 2 The change in a body s velocity due to an applied force is in the same direction as the force and proportional to it, but is inversely proportional to the body s mass. F = m a (Force = rate of change of momentum) Newton s Laws of Motion 3) For every force, there is an equal force in the opposite direction, the so-called reaction force. 6
Force from elevator Equal and opposite force (Newton s 3rd) Force from gravity (on you) Newton s Laws of Motion all reflect the conservation of momentum! 1. Newton s 1st law: an individual object s momentum will not change if it is left alone. 2. Newton s 2nd law: a force can change an object s momentum, but... 3. another equal and opposite force simultaneously changes some other object s momentum by a precisely opposite amount (Newton s 3rd law). Balance in the Universe The Force of Gravity Newton s third law saves us from accelerating away: For any force that doesn t result in an acceleration, there always is an equal and opposite reaction force. Box pushes down on table due to gravity. Table pushes back on box Any mass will exert an attractive force on every other mass. I m pulling you towards me, and you re pulling me towards you. You re force on me is equal to, but in the opposite direction of, my force on you. This is the force of gravity, one of the four fundamental forces in nature. The quantitative properties of this force were first recognized by Isaac Newton... 7
Newton s Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects. (G = the gravitational constant, a constant of nature) Two equal masses separated by distance d exert a force F on each other due to gravity. How large would the gravitational attraction be if the distance between them was doubled? 1. 1/4 F 2. 1/2 F 3. The force would be the same. 4. 2 F 5. 4 F If the Sun suddenly collapsed into a black hole with the same mass but 10 times smaller diameter, how would the Earth s orbit change? 1. It would become 10 times smaller. 2. It would become 100 times smaller. 3. The Earth would plunge into the black hole. 4. The Earth would spiral into the black hole. 5. Nothing would change. 8