Quantum Theory

1. Quantum Theory

2. Birth of Quantum Theory • A light packet is called a quantum • A quantum is the small bit of light energy that is sent by electrons when they accelerate. • Although light has wave-like properties – it has a frequency and a wavelength – it also has particle-like properties. For this reason, a light quantum is also called a photon • A photon has kinetic energy, given by E = hf. It also has momentum. • Unlike a wave, which can be increased or decreased in intensity by any degree, a photon cannot be halved or increased by a fractional amount. It is a discrete (whole number) quantity of light.

3. Quantum Theory • In the real world, we are surrounded by zillions upon kabillions of light waves of all kinds. We don’t experience single photons, ever. So we don’t notice their discreteness. • When we consider the atomic world, though , their discrete nature becomes important to understanding what we see.

4. The Electron Volt The usual unit of energy, the Joule, is too big for our purposes We use the electron volt (eV) instead 1eV = the amount of work it takes to move an electron through a potential of 1V. If we have two parallel plates with 1V between them, it would take 1eV of energy to move an electron from the positive plate to the negative plate. 1eV = 1.6 x 10-19J

5. Quantum Theory • Quantum Theory has some extreme and bizarre consequences, but it also explains a lot of discrepancies in physics • One discrepancy is with Rutherford’s model of the atom.

6. Rutherford’s Atom • Rutherford’s atom consists of a proton and an electron. • The electron orbits the proton like a satellite orbits the earth. • Like a satellite, the electron can orbit at any distance and any speed. • All is well with this except…

7. Rutherford’s Atom • The electron is accelerating since it is going in a circle. The acceleration is given by v2/r • Accelerating electrons emit electromagnetic waves • So electrons should be radiating light all of the time! • Also, as they radiate light, they should be losing energy, slowing down and spiraling into the centre. • Atoms should only last for a nanosecond before collapsing in a burst of light.

8. Rutherford’s Atom Part II • The second problem with Rutherford’s model: • Atoms radiate light when heated • The frequencies of light emitted is called an element’s spectrum. Here is hydrogen’s emission spectrum: • Atoms will emit very specific frequencies, and nothing in between. This is hard to explain. It is akin to a person being able to sing only three notes and nothing in between. Why the gaps?

9. Bohr’s Atomic Model • To solve these and other problems, Niels Bohr added quantum theory to the Rutherford model. He created the idea of orbital shells. • Just as light is quantized, so are orbits. • For reasons Bohr could not fathom, electrons cannot travel at any orbital radius. Like steps in a staircase, orbits are not continuous, they are discrete. • Bohr considered orbits like resonant lengths of a tuning fork in a resonant tube. The tube resonates only at specific lengths, and nothing in between.

10. Bohr’s Atomic Model • Bohr recognized that higher orbits had higher potential energy. • When an electron jumps from a higher orbit to a lower one, it emits a photon. Since only certain orbits are allowed, only certain energies can be given to photons being emitted. Each photon would have a specific energy, therefore a specific frequency. This explains why an element only shows specific lines.

11. Bohr’s Atomic Model • Why don’t electrons collapse into the centre? According to Bohr, there is a minimum radius possible. • Returning to our tuning fork analogy, the smallest length of tube that will resonate is called the fundamental. For an electron, the fundamental is the first orbital. The electron doesn’t collapse into the nucleus because it can’t, it is already in the smallest orbit allowed.

12. Bohr’s Success • Bohr’s quantization of electron orbits didn’t thrill a lot of people, but on paper it worked. It gave the right predictions to the unique spectral patterns produced by the elements.