E photon = -13.6 eV / 22 – (-13.6 eV / 12) = 10.2 eV, or 1.63x10-18 J QUESTION: According to Bohr’s model, which of the following wavelengths will not be absorbed by an electron in the first orbit? A. 142 nm, B. 122 nm, C. 97.5 nm, D. 94.0 nm According to Bohr: E of nth orbit = (-13.6 eV) / n2 E photon = E higher orbit - E lower orbit For transition from n=1 to n=2: E photon = -13.6 eV / 22 – (-13.6 eV / 12) = 10.2 eV, or 1.63x10-18 J SCRIPT According to Bohr’s model, which of the following wavelengths will not be absorbed by an electron in the first orbit? A. 142 nm, B. 122 nm, C. 97.5 nm, D. 94.0 nm PAUSE CLICK According to Bohr, the energy of an electron in the nth orbit of hydrogen is –13.6 electron volts, divided by the square of n. HIGHLIGHT formula An atom will absorb electromagnetic radiation if the energy of the photon is equal to the energy gap between two allowed orbits. Let’s calculate the energy of a photon that would excite an electron from the first orbit to the second orbit: CLICK The energy of the photon will be equal to… The energy of the electron if it were in the second orbit… HIGHLIGHT Minus the energy of the electron in the first orbit. The energy of the electron in the second orbit is –13.6 electron volts divided by 2 squared HIGHLIGHT And The energy of the electron in the first orbit is –13.6 electron volts divided by 1 squared CLICK This gives us a value of 10.2 electron volts for the energy of the photon. We can convert this to Joules…. CLICK Our conversion factor here is based on one electron volt being equivalent to 1.60x10-19 joules. HIGHLIGHT terms as they are called out 10.2 electron volts, times 1.60x10^-19 J over 1 electron volt Equals 1.6x10^-19 joules SCRIPT CONTINUED ON NEXT SLIDE

For n=1 to n=2: E of photon = 1.63x10-18 J QUESTION: According to Bohr’s model, which of the following wavelengths will not be absorbed by an electron in the first orbit? A. 142 nm, B. 122 nm, C. 97.5 nm, D. 94.0 nm For n=1 to n=2: E of photon = 1.63x10-18 J E = hc/, where h=6.63x10-34 Js, c=3.00x108 m/s SCRIPT, SLIDE 2 Now that we have the energy of the photon, we can calculate the wavelength. The energy of a photon is related to its wavelength according to the equation E Equals h times c divided by the wavelength lambda In this equation, h is Planck’s constant, which has a value of 6.63x10^-34 joule second And c is the speed of light, which is 3.00x10^8 meters per second CLICK We can rearrange the equation to solve for lambda. HIGHLIGHT symbols and numbers as they are called out Lambda equals h times c, divided by the photon energy, This gives us a wavelength of 1.22x10^-7 meters, or 122 nanometers. Therefore, choice B, 122 nanometers, will be absorbed by the electron CLICK SCRIPT CONTINUED ON NEXT SLIDE

QUESTION: According to Bohr’s model, which of the following wavelengths will not be absorbed by an electron in the first orbit? A. 142 nm, B. 122 nm, C. 97.5 nm, D. 94.0 nm 12: 122 nm 13: 103 nm 14: 97.5 nm 15: 94.0 nm Etc. 1: 91.4 nm 13: 103 nm SCRIPT CLICK CLICK Since 122 nanometers will be absorbed, choice B is not the correct answer. We’re looking for the wavelength that will NOT be absorbed. We expect transitions to higher orbits to involve higher photon energies and shorter wavelengths. Since choice A --- 142 nanometers --- is the only wavelength longer than 122 nm, we can be sure that it will NOT be absorbed. The correct answer is A. If you want to convince yourself, you can do a similar calculation for the transition to the third orbit CLICK You should find that a shorter wavelength of 103 nanometers will be required. CLICK If you calculate wavelengths for transitions to even higher orbits, these are what you’ll find. You will note that choice C, 97.5 nanometers, will promote an electron from orbit 1 to orbit 4. And Choice D, 94.0 nanometers will promote an electron from orbit 1 to orbit 5. The required wavelengths get shorter, but you will find that the numbers will converge to 91.4 nanometers. That’s because the gaps between adjacent orbits become smaller and smaller as n increases. This entire series of wavelengths are experimentally observed and is known as the Lyman series. Bohr’s model attributes these to transitions to or from the first orbit. CALLOUT “Lyman series” pointing to list of wavelengths PAUSE END RECORDING 12: 122 nm

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