Quantum Physics ISAT 241 Analytical Methods III Fall 2003 David J. Lawrence
Introduction to Quantum Physics • To explain thermal radiation, called “Blackbody Radiation”, Max Planck in 1900 proposed that: • The atoms and molecules of a solid absorb or emit energy in discrete units or packets called “quanta” or “photons”. • In doing so, they “jump” from one “quantum state” to another.
Introduction to Quantum Physics • In the late 1800’s, experiments showed that light incident on metallic surfaces can sometimes cause electrons to be emitted from the metal. • This “Photoelectric Effect” was explained by Einstein in 1905. • In his explanation, Einstein assumed that light, or any electromagnetic wave, can be considered to be a stream of photons.
Introduction to Quantum Physics • The photon picture of light and all other electromagnetic radiation is as follows: hf
Introduction to Quantum Physics • Each photon has an energy • h = 6.626 ´ 10-34 J × s = Planck’s constant = 4.136 ´ 10-15 eV ×s • eV = the “electron volt” = an energyunit • 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 = 1.602 ´ 10-19 J
metal plate glass tube The Photoelectric Effect • Light incident on the surface of a piece of metal can eject electrons from the metal surface. • The ejected electrons are called “photoelectrons”.
metal plate A V The Photoelectric Effect • Apparatus for studying the Photoelectric Effect: C E Variable power supply
C metal plate E A V Variable power supply The Photoelectric Effect • Photoelectrons can flow from plate E (the emitter) to plate C (the collector).
Serway & Jewett,Priciples of Physics Figure 28.5
The Photoelectric Effect Current high intensity light • Experimental results: low intensity light Applied Voltage (DV) -DVs
Serway & Jewett,Priciples of Physics Figure 28.6
The Photoelectric Effect • Experimental results: • If collector “C” is positive, it attracts the photoelectrons. • Current increases as light intensity increases. • If DV 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 |DV| will reach plate C. (e = 1.602 ´ 10-19 C)
The Photoelectric Effect • Experimental results: • If the applied voltage is - DVs (or more negative), all electrons are prevented from reaching C. • DVs is called the “stopping potential”. • The maximum kinetic energy of the emitted photoelectrons is related to the stopping potential through the relationship: Kmax= e DVs
The Photoelectric Effect • Several features could not be explained with “classical” physics or with the wave theory of light: • No electrons are emitted if the frequency of the incident light is below some “cutoff frequency”, fc, no matter how intense (bright) the light is. • The value of fc depends on the metal. • Kmax is independent of light intensity. • Kmax increases with increasing light frequency. • Photoelectrons are emitted almost instantaneously.
The Photoelectric Effect • Einstein explained the photoelectric effect as follows: • A photon is so localized that it gives all its energy (hf) to a single electron in the metal. • The maximum kinetic energy of liberated photoelectrons is given by Kmax = hf - f • f is a property of the metal called the work function. • f tells how strongly an electron is bound in the metal.
The Photoelectric Effect • Interpretation: • The photon energy (hf) must exceed f in order for the photon to eject an electron (making it a “photoelectron”). • If incident light with higher frequency is used, the ejected photoelectrons have higher kinetic energy. • “Brighter” light means more photons per second. • More photons can eject more photoelectrons. • More photoelectrons means more current.
The Photoelectric Effect • The photon energy (hf) must exceed f in order for the photon to eject an electron. • The frequency for which hf = f is called the “cutoff frequency”. f must exceed fc in order for photoelectrons to be emitted.
The Photoelectric Effect • The cutoff frequency corresponds to a “cutoff wavelength”. l must be less thanlc in order for photoelectrons to be emitted.
Bohr’s Quantum Model of the Atom • Atoms of a given element emit only certain special wavelengths (colors), called “spectral lines”. • Atoms only absorb these same wavelengths. • Neils Bohr (1913) described a model of the structure of the simplest atom (hydrogen) that explained spectral lines for the first time. • This model includes quantum concepts.
-e - Fe + +e v r Bohr’s Quantum Model of the Atom • Hydrogen consists of 1 proton and 1 electron. • The electron moves in circular orbits around the proton under the influence of the attractive Coulomb force.
- + 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. Þ Its energy is constant.
- + Bohr’s Quantum Model of the Atom • 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 • The frequency of the light that is emitted is related to the change in the atom’s energy by the equation where Ei = energy of the initial state Ef = energy of the final state Ei > Ef
Bohr’s Quantum Model of the Atom • The size of the stable or “allowed” electron orbits is determined by a “quantum condition”
Bohr’s Quantum Model of the Atom • The radii of the allowed orbits are given by h 2p h = “h-bar” = N×m2 C2 ke = 8.99 ´ 109 = “the Coulomb constant” m = mass of an electron e = charge of an electron
We get the smallest radius when n=1 h2 mkee2 r1 = ao = = 0.529 Å = 0.0529 nm = the “Bohr radius” rn = n2 ao = 0.0529 n2 (nm) Bohr’s Quantum Model of the Atom rn is said to be “quantized”, i.e., it can only have certain special allowed values.
( ) kee2 2ao 1 n2 n = 1, 2, 3, ... = En = Bohr’s Quantum Model of the Atom • “Allowed” values of energy of H atom = allowed energy levels of H atom
n = 1 E1 = -13.6 eV “ground state” -13.6 22 n = 2 E2 = = -3.40 eV “first excited state” -13.6 32 n = 3 E3 = = -1.51 eV “second excited state” 8 8 n Þ r Þ E Þ 0 8 8 Bohr’s Quantum Model of the Atom • En is also “quantized”, i.e., it can only have certain special allowed values.