Chapter 29 - Particles and Waves

1.Who won the Nobel prize for his explanation of the photoelectric effect? A.Planck B.Bohr C.De Broglie D.Einstein 2.The minimum amount of energy to free an electron from a piece of metal is called: A.The electron volt B.The work function C.The threshold energy D.The quantum energy

The Photon Model of Light The photon model of light consists of three basic postulates: 1. Light consists of discrete, massless units called photons. A photon travels in vacuum at the speed of light, 3.00 × 10 8 m/s. 2. Each photon has energy where f is the frequency of the light and h is a universal constant called Planck’s constant. The value of Planck’s constant is h = 6.63 × 10 –34 J s. 3. The superposition of a sufficiently large number of photons has the characteristics of a classical light wave.

Photon Model of Light Although the ideas of the photon model of light are attributed to Einstein, the first work suggesting energy could be quantized was done by Max Planck, while studying blackbody radiation curves.

13.3 Radiation Radiation is the process in which energy is transferred by means of electromagnetic waves. A material that absorbs completely is called a perfect blackbody. The absorbed energy is emitted by vibrating atoms of the blackbody object. At the beginning of the 20 th century, scientists, including Planck, studied the spectrum of EM energy emitted by blackbodies. The energy emitted did not agree with theoretical models using classical physics.

Photon Model of Light In 1900, Planck was able to solve the problem by constraining the energy of the vibrating atoms to be a series of discrete, or “quantized” values, such that:

Photon Model of Light Planck’s conclusions implied that the lowest energy carried by EM waves was equal to hf. Einstein was the first to take Planck’s idea seriously.

The energy of a photon

Compare the energy of a photon of red light with that of a photon of blue light: A. The red photon has more energy because it has a greater wavelength B.The blue photon has more energy because it has a greater frequency C. All photons have the same energy, regardless of frequency D. Photon energy depends on light intensity, not color.

Compare the energy of a photon of red light with that of a photon of blue light: A. The red photon has more energy because it has a greater wavelength B.The blue photon has more energy because it has a greater frequency C. All photons have the same energy, regardless of frequency D. Photon energy depends on light intensity, not color.

The electron volt The amount of energy, hf of a photon is a very small number in Joules It is time to introduce the electron volt, which is defined as the amount of potential energy an electron gains (or loses) when it moves through a potential difference of one volt :

The electron volt Electron volts are energy units, not voltage units (unfortunate choice of names if you ask me, but nobody did). In electron volt units, h = 4.14 x eVs

29.3 Photons and the Photoelectric Effect Experimental evidence that light consists of photons comes from a phenomenon called the photoelectric effect.

The Photoelectric Effect In 1886 it was first discovered by Hertz, that a negatively charged electroscope could be discharged by shining ultraviolet light on it. In 1899, Thomson showed that the emitted charges were electrons. The emission of electrons from a substance due to light striking its surface came to be called the photoelectric effect. Around 1900, Lenard observed that the photoelectric effect was not dependent on light intensity, but rather on light frequency, which seemed to contradict classical physics. In 1905, Einstein used Planck’s hypothesis of quantized energy to explain the contradiction. He won a Nobel Prize for his work.

Einstein’s Postulates Einstein framed three postulates about light quanta and their interaction with matter: 1.Light of frequency f consists of discrete quanta, each of energy E = hf, where h is Planck’s constant h = 6.63 × 10 −34 J s. Each photon travels at the speed of light c = 3.00 × 10 8 m/s. 2.Light quanta are emitted or absorbed on an all- or-nothing basis. A substance can emit 1 or 2 or 3 quanta, but not 1.5. Similarly, an electron in a metal can absorb only an integer number of quanta. 3.A light quantum, when absorbed by a metal, delivers its entire energy to one electron.

29.3 Photons and the Photoelectric Effect When light shines on a metal, a photon, with energy hf, can give up its energy to an electron in that metal. The minimum energy required to remove the least strongly held electrons is called the work function, W 0. The value of W 0 is specific to the metal. The photon energy comes in discrete packets called quanta, (plural for quantum).

29.3 Photons and the Photoelectric Effect KE max depends on the frequency of light incident on the metal. The minimum frequency necessary for an electron to leave the lattice structure of the metal (with 0 KE) is the threshold frequency, f 0. Electrons will not leave the metal at f < f 0. W 0 = hf 0

29.3 Photons and the Photoelectric Effect Example 2 The Photoelectric Effect for a Silver Surface The work function for a silver surface is 4.73 eV. Find the minimum frequency that light must have to eject electrons from the surface. It is not necessary to change from electron volts to Joules to solve this problem. This is actually a frequency in the ultraviolet spectrum, not visible.

The speed of an electron Light of 300 nm is incident on sodium metal, W 0 = 2.75 eV. What is the maximum speed for an electron leaving the metal? 1.Change wavelength to frequency: f = 1.00 x Hz, so hf = 4.14 eV 2.K max = hf – W 0 using values given above 3.K max =1.39 eV or 2.22 x J

The speed of an electron Light of 300 nm is incident on sodium metal, W 0 = 2.75 eV. What is the maximum speed for an electron leaving the metal? 1.K max =2.22 x J 2.Now find speed, using ½ mv 2 (m is mass of electron, not mass of Na atom) 3. v = 6.99 x 10 5 m/s

29.3 Photons and the Photoelectric Effect