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Determining Wavelengths for Spectral Series in Hydrogen

Determining Wavelengths for Spectral Series in Hydrogen. or Why it’s a good idea to pay attention in class instead of falling asleep and then trying to figure out what on EARTH is going on…. Let’s begin with quantum numbers and what they mean….

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Determining Wavelengths for Spectral Series in Hydrogen

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  1. Determining Wavelengths for Spectral Series in Hydrogen or Why it’s a good idea to pay attention in class instead of falling asleep and then trying to figure out what on EARTH is going on…

  2. Let’s begin with quantum numbers and what they mean… Can be any value from < 1 to n > where “n” can equal ∞ Designates the overall size of an orbital (cloud) Is the main determinant of orbital energy Often designated by shells where K = 1, L = 2, M = 3, N = 4, et cetera. l…Azimuthal Quantum Number (shape) Can be any value from < 0 to n-1 > Designates the overall shape of an orbital Is a contributor of orbital energy for higher values of l , and is sometimes referred to as “angular orbital momentum” All electrons with same value are said to be in the same subshell Often designated by axes of symmetry where 0 = s (sphere), 1 = p (pair) or “polar”, 2 = d (diffuse), 3 = f (fine) ml …Magnetic Quantum Number (orientation) n…Principal Quantum Number (shell) Can be any value from < - l to + l > Designates the spatial orientation of the orbital Does not greatly contribute to orbital energy (EXCEPT in magnetic fields) The number of mlvalues within a shell designates the number of orbitals within the subshell… For example, if l = 0, then mlpossibilities = 1 (just 0), but if l = 1, then mlpossibilities = 3 ( -1, 0, and +1) ms …Magnetic Spin Number (up or down) Can be either < +½ or - ½> for each mlvalue Can be explained by thinking of the electron as rotating (vs. orbiting) Can be designated by either clockwise spin or anti-clockwise spin Unpaired spin is responsible for paramagnetism and ferromagnetism

  3. Hydrogen • For hydrogen, the experimentally determined value of allowed energy level at n = 1 for an electron is E0 = -13.6 eV. That is to say, if an electron were taken from the ground state to where the electron where no longer under the influence of the proton, then you would need 13.6 eV of energy to ionize the atom. • The formula to determine subsequent energies at higher levels is En = E0 / n2 • Therefore, at n = 2 your E = 3.40 eV and for n = 6 then E = 0.378 eV. (Try the math yourself.)

  4. Calculating Energies Associated with Transitions • The first step is to recognize that according to Planck E = h*f • The second step is knowing that since the charge for an electron is -1.602 E (-19) C, then the energy to move an electron through a potential difference of one volt (definition of 1 eV) must equal 1.602 E (-19) J.

  5. Using Energy to Calculate f • Now if you find the difference between say the 6th energy level and the 2nd, then the difference would be 3.022 eV.(from the slide before the previous slide) • Convert this Energy in eV to Joules where 3.022 eV * 1.602 E (-19) J = 4.841 E (-19) J 1 eV • Re-arrange Planck’s equation to where f = E / h and substitute values so that now f = 4.841 E (-19) J = 7.306 E (14) s-1 or just 7.306 E (14) Hz 6.626 E (-34) J *s

  6. Using f to calculate λ • Now that you calculated frequency to equal to 7.306 E (14) Hz, use the value of c (speed of light) to calculate its wavelength. • Since c = f * λ, then λ = c/f or with values λ = (3.00 E (8)m/s) / (7.306 E (14) Hz to give you a value of 4.11 E (-7) or 411nm. • This value is just within the visible spectrum since values range from 400 nm for violet to 750 nm for dark red.

  7. What the hell do I do now, Calderón? • For your Homework Set 5: Energy Values for n = 1 to 4, you will have to find the energies for each transition and the corresponding wavelengths. • To do this, simply calculate the values for each energy level 1 through 4. • Now set up to where you determine the differences between ∞ to 1 (which is just the value of 1 since the energy at ∞ is by definition 0), 4 to 1, 3 to 1, and 2 to 1. This tells you how what wavelength of photons are emitted as electrons fall back to the first energy level. • You will do the same for the differences between ∞ to 2 (which is just the value of 2 since the energy at ∞ is by definition 0), 4 to 2, and 3 to 2. This is a separate band for wavelengths produced as electrons fall to the second energy level. • Now do the same between ∞ to 3 and 4 to 3. This is a separate band for wavelengths produced as electrons fall to the third energy level. • Finish off with transitions from ∞ to 4. Does this produce visible light?

  8. It’s called reading…and tutoring. • Read through chapter 27, but don’t get too in-depth. Look at the diagrams and what is familiar. • Come in for tutoring if you really need it. • Pray. • Shalom alechem, ya’ll.

  9. The Visible Portion of the EMSpectrum Top image courtesy of www.szote.u-szeged.hu Bottom image courtesy of www.physicalgeography.net

  10. Sun approximating blackbody radiation at about 5800 KNotice the absorption lines which are caused the suns corona. Approximate color emitted Graphic courtesy of http://ioannis.virtualcomposer2000.com/spectroscope/elements.html

  11. Emission Spectra of Various StarsCourtesy of http://members.cox.net/rigelsys/downloads/RS-spectroscope_man.pdfBellatrix is: γ-Orionis (blue) Sirius: α-Canis Majoris (red) Procyon α-Canis Minoris (yellow)Aldebaran: α-Taurus (red-orange) Betelgeuse: α -Orionis (light red)

  12. Hydrogen at 1800 K Graphic courtesy of http://ioannis.virtualcomposer2000.com/spectroscope/elements.html Approximate color emitted Graphic courtesy of http://astro.u-strasbg.fr/~koppen/discharge/

  13. Helium at 2600 K Graphic courtesy of http://ioannis.virtualcomposer2000.com/spectroscope/elements.html Approximate color emitted Graphic courtesy of http://astro.u-strasbg.fr/~koppen/discharge/

  14. Oxygen at ?? Graphic courtesy of http://ioannis.virtualcomposer2000.com/spectroscope/elements.html Approximate color emitted Graphic courtesy of http://astro.u-strasbg.fr/~koppen/discharge/

  15. Neon at 1875 K Graphic courtesy of http://ioannis.virtualcomposer2000.com/spectroscope/elements.html Approximate color emitted Graphic courtesy of http://astro.u-strasbg.fr/~koppen/discharge/

  16. Mercury at ?? Graphic courtesy of http://ioannis.virtualcomposer2000.com/spectroscope/elements.html Approximate color emitted Graphic courtesy of http://astro.u-strasbg.fr/~koppen/discharge/

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