E photon = h , h = Planck’s constant = 6.63x10-34 J s  = Frequency QUESTION: What is the energy of a photon of ultraviolet radiation with a wavelength 250 nm? A. 5.0 eV, B. 2.5 eV, C. 4.0x10-2 eV 1 eV = 1 electron volt = energy gained by an electron that is accelerated through a potential difference of one volt = (charge of electron) (potential difference) = (1.60x10-19 C) ( 1 V) = 1.60x10-19 CV 1 CV = 1 J C=Coulomb; V=Volt; J=Joule E photon = h , h = Planck’s constant = 6.63x10-34 J s  = Frequency = c/ = (3.00x108 m/s) / (250x10-9 m) = 1.20x1015 s-1 E photon = (6.63x10-34 J s) (1.20x1015 s-1) = 7.96x10-19 J Conversion factor: 1 eV = 1.60x10-19 J E photon = 7.96x10-19 J x (1 eV / 1.60x10-19 J) = 4.98 eV  5.0 eV SCRIPT: What is the energy of a photon of ultraviolet radiation with a wavelength 250 nm? A. 5.0 eV, B. 2.5 eV, C. 4.0x10-2 eV CLICK The energy of a photon is directly proportional to the frequency. Specifically, it is equal to Planck’s constant, h HIGHLIGHT h times the frequency nu HIGHLIGHT nu The value of Planck’s constant is 6.63x10^-34 joule second… HIGHLIGHT We’re not given the frequency in the question, but we are given the wavelength, which we can use to calculate the frequency. The frequency of an electromagnetic wave is equal to the speed of the wave, c.. Divided by the wavelength, lambda… The speed of electromagnetic waves is 3.00 x 10^8 meters per second. HIGHLIGHT And we’re given a wavelength of 250 nanometers --- highlight 250 nm. For unit consistency, the wavelength value we plug in to our formula must be in meters. So, we change 250 nanometers to 250 x 10^-9 m, since a nanometer is equal to 10^-9 meter CALLOUT “1 nm = 10-9 m” pointing to “10-9 m” When we do the calculation … Meters cancel out CLICK CLICK Punching these numbers into a calculator, we find that the frequency is 1.20x10^15 cycles per second. We can now calculate the energy of the photon….which is equal to Planck’s constant, 6.63x10^-34 joule second Times the frequency, which we just calculated to be 1.20x10^15 per second Second and per per second cancel out. And we get an answer of 7.96x10^-19 joules. Photon energies tend to be small numbers like this… we it is more convenient to express it in a smaller unit. The most commonly used unit is electron volts. One electron volt is equivalent to 1.60x10^-19 joules. AN electron volt is the energy gained by an electron when it is accelerated through a potential difference of 1 volt. This energy is equal to the charge of the electron, 1.60x10^-19 Coulombs, times the potential difference of 1 volt, Or 1.60x10^-19 Coulomb volt. One Coulomb volt is equal to one joule. CLICK To convert our answer to electron volts, we multiply it HIGHLIGHT by one electron volt HIGHLIGHT divided by 1.6x10^-19 joules This gives us an answer of 4.98 electron volts, which we round off to 5.0 electron volts. There are two significant digits in 250 nm. So only keep two significant digits in our final answer. Note that we kept an extra digit in the intermediate results. This is so that we do not build up round off errors. The correct answer is A. PAUSE CLICK END RECORDING.

Video ID: 2-1-5 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08