Topic 13 Quantum and Nuclear physics Atomic spectra and atomic energy states How do you excite an atom? 1. Heating to a high temperature 2. Bombarding with electrons 3. Having photons fall on the atom I’m excited! Atomic spectra When a gas is heated to a high temperature, or if an electric current is passed through the gas, it begins to glow. Light emitted cathode Low pressure gas anode electric current Emission spectrum If we look at the light emitted (using a spectroscope) we see a series of sharp lines of different colours. This is called an emission spectrum. Absorption Spectrum Similarly, if light is shone through a cold gas, there are sharp dark lines in exactly the same place the bright lines appeared in the emission spectrum. Light source gas Some wavelengths missing! Why? Scientists had known about these lines since the 19th century, and they had been used to identify elements (including helium in the sun), but scientists could not explain them. Rutherford At the start of the 20th century, Rutherford viewed the atom much like a solar system, with electrons orbiting the nucleus. Rutherford However, under classical physics, the accelerating electrons (centripetal acceleration) should constantly have been losing energy by radiation (this obviously doesn’t happen). Radiating energy Niels Bohr In 1913, a Danish physicist called Niels Bohr realised that the secret of atomic structure lay in its discreteness, that energy could only be absorbed or emitted at certain values. At school they called me “Bohr the Bore”! The Bohr Model Bohr realised that the electrons’ angular momentum is an integral (whole number) multiple of the unit h/2π. This meant that the electron could only be at specific energy levels (or states) around the atom. The Bohr Model We say that the energy of the electron (and thus the atom) can exist in a number of states n=1, n=2, n=3 etc. (Similar to the “shells” or electron orbitals that chemists talk about!) n=1 n=2 n=3 The Bohr Model The energy level diagram of the hydrogen atom according to the Bohr model Energy eV 0 High energy n levels are very close to each other n=5 n=4 n=3 n=2 Electron can’t have less energy than this -13.6 n = 1 (the ground state) The Bohr Model An electron in a higher state than the ground state is called an excited electron. It can lose energy and end up in a lower state. Energy eV 0 High energy n levels are very close to each other n=5 n=4 Wheeee! n=3 n=2 -13.6 n = 1 (the ground state) Atomic transitions If a hydrogen atom is in an excited state, it can make a transition to a lower state. Thus an atom in state n = 2 can go to n = 1 (an electron jumps from orbit n = 2 to n = 1) Energy eV 0 n=5 n=4 Wheeee! n=3 electron n=2 -13.6 n = 1 (the ground state) Atomic transitions Every time an atom (electron in the atom) makes a transition, a single photon of light is emitted. Energy eV 0 n=5 n=4 n=3 electron n=2 -13.6 n = 1 (the ground state) Atomic transitions The energy of the photon is equal to the difference in energy (ΔE) between the two states. It is equal to hf. ΔE = hf Energy eV 0 n=5 n=4 n=3 electron n=2 ΔE = hf -13.6 n = 1 (the ground state) The Lyman Series Transitions down to the n = 1 state give a series of spectral lines in the UV region called the Lyman series. Energy eV 0 n=5 n=4 n=3 n=2 -13.6 n = 1 (the ground state) Lyman series of spectral lines (UV) The Balmer Series Transitions down to the n = 2 state give a series of spectral lines in the visible region called the Balmer series. Energy eV 0 n=5 n=4 n=3 n=2 Balmer series of spectral lines (visible) -13.6 n = 1 (the ground state) UV The Pashen Series Transitions down to the n = 3 state give a series of spectral lines in the infra-red region called the Pashen series. Energy eV 0 n=5 n=4 n=3 Pashen series (IR) n=2 visible -13.6 n = 1 (the ground state) UV Emission Spectrum of Hydrogen The emission and absorption spectrum of hydrogen is thus predicted to contain a line spectrum at very specific wavelengths, a fact verified by experiment. Which is the emission spectrum and which is the absorption spectrum? Pattern of lines Since the higher states are closer to one another, the wavelengths of the photons emitted tend to be close too. There is a “crowding” of wavelengths at the low wavelength part of the spectrum Energy eV 0 n=5 n=4 n=3 n=2 Spectrum produced -13.6 n = 1 (the ground state) Limitations of the Bohr Model 1. Can only treat atoms or ions with one electron 2. Does not predict the intensities of the spectral lines 3. Inconsistent with the uncertainty principle (see later!) 4. Does not predict the observed splitting of the spectral lines The “electron in a box” model! Hi! I’m Erica the electron ☺ The “electron in a box” model! • Imagine an electron is confined within a linear box length L. ☺ L The “electron in a box” model! • According to de Broglie, it has an associated wavelength λ = h/p ☺ L The “electron in a box” model! • Imagine then the electron wave forming a stationary wave in the box. L The “electron in a box” model! • Therefore we have a stationary wave with nodes at x = 0 and at x = L (boundary conditions) L The “electron in a box” model! • The wavelength therefore of any stationary wave must be λ = 2L/n where n is an integer. L The “electron in a box” model! • The momentum of the electron is thus • P = h/λ = h/2L/n = nh/2L The “electron in a box” model! • The kinetic energy is thus = p2/2m = (nh/2L)2/2m = n2h2/8mL2 The “electron in a box” model! • Ek = n2h2/8mL2 ☺ L Energy states This can be thought of like the allowed frequencies of a standing wave on a string (but this is a crude analogy). Erwin Schrödinger The many problems with the Bohr model were corrected by Erwin Schrödinger, an Austrian physicist. d2Ψ/dx2 = -8π2m(E – V)Ψ/h2 The Schrödinger equation I like cats! Erwin Schrödinger Schrödinger introduced the wave function, a function of position and time whose absolute value squared is related to the probability of finding an electron near a specific point in space and time. I don’t believe that God plays dice! Erwin Schrödinger In this theory, the electron can be thought of as being spread out over a large volume and there are places where it is more likely to be found than others! This can be thought of as an electron cloud. Rubbish! Wave function Ψ = (2/L)½(πnx/L) where n is the state, x is the probability of finding the electron and L is the “length” of the orbital. From this we also get the energy to be EK = h2n2/8meL2 Beware! I’m used to the idea of waves, so I like using Schrödinger’s model This wave function is only a mathematical model that fits very well. It also links well with the idea of wave particle duality (electron as wave and particle). But it is only one mathematical model of the atom. Other more elegant mathematical models exist that don’t refer to waves, .but physicists like using the wave model because they are familiar with waves and their equations. We stick with what we are familiar! Heisenberg Uncertainty Principle Heisenberg Uncertainty Principle • It is not possible to measure simultaneously the position AND momentum of a particle with absolute precision. ΔxΔp ≥ h/4π Also ΔEΔt ≥ h/4π That’s it for Quantum physics! Next week we’ll be looking at nuclear physics! Let’s try some questions.