Quantum Physics ISAT 241 Analytical Methods III Fall 2003 David J. Lawrence

Introduction to Quantum Physics u To explain thermal radiation, called “Blackbody Radiation”, Max Planck in 1900 proposed that: u The atoms and molecules of a solid absorb or emit energy in discrete units or packets called “quanta” or “photons”. u In doing so, they “jump” from one “quantum state” to another.

Introduction to Quantum Physics u In the late 1800’s, experiments showed that light incident on metallic surfaces can sometimes cause electrons to be emitted from the metal. u This “Photoelectric Effect” was explained by Einstein in u In his explanation, Einstein assumed that light, or any electromagnetic wave, can be considered to be a stream of photons.

Introduction to Quantum Physics u The photon picture of light and all other electromagnetic radiation is as follows: h fh f

Introduction to Quantum Physics u Each photon has an energy  h =  J  s = Planck’s constant =  eV  s u eV = the “electron volt” = an energy unit u 1 eV is defined as the kinetic energy that an electron (or proton) gains when accelerated by a potential difference of 1 V.  1 eV =  10  19 J

The Photoelectric Effect u Light incident on the surface of a piece of metal can eject electrons from the metal surface. u The ejected electrons are called “photoelectrons”. metal plate glass tube

The Photoelectric Effect u Apparatus for studying the Photoelectric Effect: metal plate A V E C Variable power supply

The Photoelectric Effect u Photoelectrons can flow from plate E (the emitter) to plate C (the collector). metal plate A V E C Variable power supply

Serway & Jewett,Priciples of Physics Figure 28.5

The Photoelectric Effect u Experimental results:  V s Current Applied Voltage (  V) high intensity light low intensity light

Serway & Jewett,Priciples of Physics Figure 28.6

The Photoelectric Effect u If collector “C” is positive, it attracts the photoelectrons. u Current increases as light intensity increases.  If  V is negative (i.e., if battery is turned around to make C negative and E positive), the current drops because photoelectrons are repelled by C.  Only those photoelectrons that have KE > e |  V| will reach plate C. (e =   C  u Experimental results:

The Photoelectric Effect  If the applied voltage is  V s (or more negative), all electrons are prevented from reaching C.   V s is called the “stopping potential”. u The maximum kinetic energy of the emitted photoelectrons is related to the stopping potential through the relationship: K max = e  V s u Experimental results:

The Photoelectric Effect u No electrons are emitted if the frequency of the incident light is below some “cutoff frequency”, f c, no matter how intense (bright) the light is. u The value of f c depends on the metal. u K max is independent of light intensity. u K max increases with increasing light frequency. u Photoelectrons are emitted almost instantaneously. u Several features could not be explained with “classical” physics or with the wave theory of light:

The Photoelectric Effect u A photon is so localized that it gives all its energy (hf) to a single electron in the metal. u The maximum kinetic energy of liberated photoelectrons is given by K max = hf    is a property of the metal called the work function.   tells how strongly an electron is bound in the metal. u Einstein explained the photoelectric effect as follows:

The Photoelectric Effect  The photon energy (hf) must exceed  in order for the photon to eject an electron (making it a “photoelectron”). u If incident light with higher frequency is used, the ejected photoelectrons have higher kinetic energy. u “Brighter” light means more photons per second. u More photons can eject more photoelectrons. u More photoelectrons means more current. u Interpretation:

The Photoelectric Effect  The photon energy (hf) must exceed  in order for the photon to eject an electron.  The frequency for which hf =  is called the “cutoff frequency”. f must exceed f c in order for photoelectrons to be emitted.

The Photoelectric Effect u The cutoff frequency corresponds to a “cutoff wavelength”. must be less than c in order for photoelectrons to be emitted.

Bohr’s Quantum Model of the Atom u Atoms of a given element emit only certain special wavelengths (colors), called “spectral lines”. u Atoms only absorb these same wavelengths. u Neils Bohr (1913) described a model of the structure of the simplest atom (hydrogen) that explained spectral lines for the first time. u This model includes quantum concepts.

Bohr’s Quantum Model of the Atom u Hydrogen consists of 1 proton and 1 electron. u The electron moves in circular orbits around the proton under the influence of the attractive Coulomb force e ee r FeFe v

Bohr’s Quantum Model of the Atom  Only certain special orbits are stable. While in one of these orbits, the electron does not radiate energy.  Its energy is constant. + -

Bohr’s Quantum Model of the Atom u Radiation (e.g., light) is emitted by the atom when the electron “jumps” from a higher energy orbit or “state” to a lower energy orbit or state. + -

Bohr’s Quantum Model of the Atom u The frequency of the light that is emitted is related to the change in the atom’s energy by the equation where E i = energy of the initial state E f = energy of the final state E i > E f

Bohr’s Quantum Model of the Atom u The size of the stable or “allowed” electron orbits is determined by a “quantum condition”

Bohr’s Quantum Model of the Atom u The radii of the allowed orbits are given by h = “h-bar” = h 2  k e = 8.99  10 9 = “the Coulomb constant” N  m 2 C 2 m = mass of an electron e = charge of an electron

Bohr’s Quantum Model of the Atom u We get the smallest radius when n=1 r 1 = a o = = Å = nm = the “Bohr radius” h 2 mk e e 2 r n = n 2 a o = n 2 (nm) r n is said to be “quantized”, i.e., it can only have certain special allowed values.

Bohr’s Quantum Model of the Atom u “Allowed” values of energy of H atom = allowed energy levels of H atom = E n = k e e 2 2a o ( ) 1n21n2 n = 1, 2, 3,...

Bohr’s Quantum Model of the Atom u E n is also “quantized”, i.e., it can only have certain special allowed values. n = 1 E 1 =  13.6 eV “ground state” n = 2 E 2 = =  3.40 eV “first excited state”  n = 3 E 3 = =  1.51 eV “second excited state”  n  8 E  0 8 r  8 8