Annihilation and pair production

Everyone has seen this equation. It's not strictly on the syllabus this year: ie you don't need to do calculations with it. However, it explains a lot. It tells us that pure energy (E) can be changed into particles of mass m. Or particles of mass m can be destroyed and turned into energy E.
This is annihilation. A positron and an electron are destroyed and two gamma ray photons are made.

• Positive and negative because charge has to add up to zero. The energy that is made has no charge.
• Equal and opposite motion so that momentum before is zero.
• Two gamma ray photons so that momentum is zero after the annihilation.
  

In reverse, two gamma ray photons can come together to make a positron and an electron. This is pair production.

Cladding

The question on the January exam about curved bit of glass with 3 rays going through (P,Q,R) raised some interesting ideas about cladding. Cladding is a layer of transparent material wrapped around the outside of the central fibre (the core). The purpose of the cladding is to stop the central glass core getting scratched. Scratched cores leak light more easily because it changes the angle of the outside wall of the glass and thus changes the angle of incidence.

Cladding makes it more difficult for the light to stay in the glass:

We will be using this equation. But note that at the critical angle, the second angle is zero.When there is no cladding, there is air around with refractive index of n = 1. So With the cladding, we get this equation:

Simple calculation will show that the critical angle becomes bigger. There are now fewer angles at which the light can hit the glass for TIR, so it is much easier for light to escape into the cladding.

Finally, be careful how you define critical angle.

• The angle of incidence for which the angle of refraction is 90 degrees.
• The minimum angle of incidence for which you get total internal reflection.
  
  
  

Making IV characteristics

In this circuit, a varaible resistor is being used to change the voltage and current through a bulb. This is not a good circuit to use for an IV characteristic. Here's why:

• Suppose the bulb has a resistance of 20 Ohms and we use a 6 Volt battery.
• The variable resistor can go from zero up to a maximum of 20 Ohms.
• When the variable resistor has zero Ohms, then the bulb will take all of the energy and the voltmeter reading will be at a maximum of 6 Volts.
• When the variable resistor has 20 Ohms, then the bulb and the resistor will have the same resistance and they will have equal shares of the energy. Voltmeter will read 3 Volts.
• Hence by using a variable resistor like this, there is a limited range of voltages you can use. In this case it is between 3V and 6V. You can't get down to 0 V.
• I suppose that if you use a variable resistor with a maximum resistance massively bigger than the bulb, you'd get a better range.

It is much better to use this set up, called a potentiometer. All 3 connections on the variable resistor (rheostat) are used and you can have all the voltages from 0V up to 6V.
This is the set up we used in class. (see IV characteristics booklet). We used a version of a potentiometer when we had the wire along the meter stick in the observation room so that every 10 cm represented 1V.

The plum pudding model

Before Geiger and Marsden did the important gold leaf experiment for Ernest Rutherford, the best idea about the inside of an atom was called the "Plum Pudding" model.

• They had just discovered the electron so they knew that there had to be negative particles inside the atom.
• If there were negatives, there had to be positive as well.
• They imagined the positive charge as being thinly smeared all over the atom. There were no definite positive particles in this model.
• The positive is supposed to be like the dough in a Christmas Pudding, and the electrons are like the raisins.

Any alpha particles fired at it should go straight through because

• alpha particles are much bigger and heavier than electrons so they would knock them out of the way.
• the positive charge is so thinly spread that there is no chance of repelling the doubly positive alpha particle.

Then the gold leaf experiment was done and Rutherford invented the Solar System model with the positive nucleus and orbitting electrons. The Plum Pudding model was consigned to the dustbin of history.

Rutherford scattering

In this experiment, a very narrow beam of alpha particles was fired at a very thin piece of gold foil.

• The thick sheets of lead are to stop the beam of alpha spreading out like the beam on a car headlight. They keep the beam narrow. The arrangement is called a collimator.
• The detector is moved around the outside of vacuum chamber and readings taken for different angles.
• The beam has to be narrow because this gives a very definite spot on the foil from which to measure the angle, as shown on the diagram below: The moment of genius was when it was decided to move the detector round onto the same side as the alpha source. No one in their right mind would expect to find alpha particles on this side, but that is excatly what they did discover. It's called backscattering. We can tell that the nucleus is positive because the positive alpha particles are repelled.
• We can tell that the nucleus is heavy by thinking of what happens in snooker when the cue ball hits a coloured ball. The cue ball stops but the coloured ball moves on. Momentum is transferred here because both balls have the same mass. However, the alpha particle bounces back and the nucleus is unmoved. This means that the nucleus is much heavier.
  
  

What happens when a photon carries too little energy?

They seem to be asking a lot of questions about what happens when a photon arrives carrying too little energy for an electron to reach the first level.

The correct answer is that NOTHING HAPPENS.

The electron does not jump up half way and then fall back. It just sits there as if nothing has happened. It does not absorb the photon at all.