Bohr’s contribution to the model of an atom KCI SEM 1 2016-17 Bohr’s contribution to the model of an atom

Some background info.

Classically, light is thought to be a wave Light or electromagnetic radiation is a wave in which - electric field oscillates perpendicular to magnetic field through space

Wavelength (symbol: , called lambda) = distance between any 2 adjacent identical points of a wave (i.e. between 2 crests or 2 troughs)

 Frequency of a wave = # of wavelengths of that wave passing by a fixed point in one second  Frequency symbol: , called nu or new  Unit: 1/second or Hertz (Hz) The shorter the wavelength, the higher the frequency The longer the wavelength, the lower the frequency

c =  x  Or c is fixed: If  increases,  will decrease Math. relationship b/t wavelength and frequency where c = 3.00 x 108 m/s = speed of light in a vacuum c =  x  Or c is fixed: If  increases,  will decrease If  decreases,  will increase http://education.jlab.org/frost/speed_of_light.html measured speed of light with chocolate

E photon = h Ephoton = h The Energy of Light Electromagnetic waves interact with matter in discrete packets, or quanta, of energy called photons. E photon = h Ephoton = h Where h is Planck’s constant and has a value of 6.626x10-34 J●s The energy of the photon depends on the wavelength or frequency. Electromagnetic radiation of long wavelength and low frequency, such as radio waves, is composed of lower-energy photons. Short-wavelength radiation with high frequencies is composed of higher-energy photons.. Photon energy is directly proportional to frequency and inversely proportional to wavelength.

Rethinking light: Light also behave as a particle 1. Blackbody radiation Widely accepted: A heated object emits light The hotter it gets, higher energy re-radiated e.g. UV, X-ray, Gamma rays  but no object does this Any body at any temperature above absolute zero will radiate to some extent, the intensity and frequency distribution of the radiation depending on the detailed structure of the body.  To begin analyzing heat radiation, we need to be specific about the body doing the radiating:  the simplest possible case is an idealized body which is a perfect absorber, and therefore also (from the above argument) a perfect emitter. For obvious reasons, this is called a “black body”. From Gammon and Ebbing: Imagine quantization is applied to energy of a moving car. Quantization of a car’s energy would mean that only certain speeds were possible. A car could travel at say 10, 20, or 30 km/hr but not at 12 or 25 km/hr. For car energies, this is unreasonable/obscene. But for atoms, quantization is the rule Planck proposed: light is not continuous as previously thought but discrete bundles of energy, called quanta E​photon​​=h h = Planck’s constant = 6.626×10​−34​​ J⋅s)

Rethinking light: Light also behave as a particle 2. The photoelectric effect: Certain frequencies of light were able to knock electrons off the surface of a specific metal Other frequencies regardless of the intensity of light, were unable to do so. The photoelectric effect: is the ejection of e- from the surface of a metal or form another material when light shines on it. Electrons are ejected, however, only when the frequency of light exceeds a certain threshold value characteristic of the particular metal. For example, although violet light will cause K metal to eject e-, no amount of red light (which has a lower frequency) has any effect. The photon that struck the metal and caused an e- to be ejected must have at least enough energy to remove the electron from the attractive forces of the metal. No matter how many photons strikes the metal (i.e. high intensity), if no single one has sufficient energy, an e- cannot be ejected.

Bohr’s Model of the Atom 1913 Danish physicist Very good resource: http://www.ck12.org/user:bwv2yw5zqgjjc3dhbi5uzxq./book/Mrs.-Evans-Chemistry-FlexBook/section/6.1/ Science is not a one-man show The work of other scientists help lay a foundation for new discoveries

Hands-on activity: emission spectra Hot gas emit light The color you see can be split into its constituent colors by a prism; these are viewed as discrete lines

Record what you observed Heated Gas Color emitted (without spectroscope) Color of emission lines from spectroscope (if applicable) Hydrogen   2. Helium 3. Neon 4. Carbon dioxide

1. What responsible for the distinctively colored lines you observed? 2. How can we explain those lines? 3. As the # of e- in the atom increases, what happens to this color pattern?

Watch emission spectrum of Hydrogen clip ( in usb Quantum folder)

Atomic emission spectra are unique for each element They can then be used as fingerprints to identify atom

Absorption vs. Emission Spectra of Hydrogen Absorption spectrum: Observed when white light passing through Hydrogen gas. The Hydrogen atom absorb very specific wavelength of radiation resulting in missing lines in the continuous spectrum. Emission spectrum: As excited electrons relax to lower energy levels, light is emitted. This release of energy explains for the color lines on the emission spectrum of hydrogen atom. Many more lines but they’re in IR and UV regions and thus are not visible. Note that the spectral lines are on the same wavelength.

Bohr set out to explain the relationship between : Emission or Line spectrum the emission lines in emission spectrum of H atom AND Hydrogen’s atomic structure Red, green, blue and violet spectral lines

Experimental evidence Bohr’s model of an atom From Max Planck: Hot matter emits electromagnetic energy as discrete packets or quanta of energy From Einstein: Matter absorbs light energy and can only absorb it in packets ( =photons) in an “all or none” manner His own: - Excited atoms emit specific wavelengths (photon) or light Electrons exist only in “ALLOWED” circular orbits. While an electron remains in one orbit, it does NOT radiate (lose) energy. Electrons can “jump” between orbits (energy levels) by absorbing or emitting photons carrying an amount of energy that is EQUAL to the difference in the energy levels of the electrons. ( i.e.photon carries higher or less than this amt of energy causes no e- transition) Bohr’s simple assumption By now Bohr has inherited the ideas that Light is quantized Spectroscopy is a powerful tool to infer about atomic structure Adding his own assumption: What if some aspects of atomic structure, such as electron orbits and energies, could only take on certain values?

The Bohr’s Model of the Atom

The Bohr’s Model of the Atom Bohr was able to calculate the energy and radii of the allowed orbits for the hydrogen atom. In Bohr’s atomic model, the orbits are numbered with n = 1 as the orbit nearest the nucleus. Bohr’s calculated radius of this orbit is 5.291 77 x 10-11 m, which is now called the Bohr radius. Because the orbit has the lowest possible energy, it is called the ground state of the atom. Energy is required to move the electron farther from the nucleus due to the attractive force of the nucleus. The distance between the orbits gets larger with each orbit.

The quantum leap Absorption of Energy = Excitation If the incoming energy is exactly equal to the difference in energy between two orbits, the electron leaps to excited state When moving within these allowed energy states (stationary states) the electron does NOT emit (release) energy. ??? If the incoming energy is a little less or greater, it passes through the atom unaffected

The quantum leap Emission of Energy = Relaxation As excited e- relaxes to lower energy level, it releases the energy difference between the two orbits in the form of electromagnetic radiation. This explains spectral lines of excited atoms and the origin of light itself. If do Efinal – E initial wavelength will be negative value

Electrical energy is absorbed and excites the electrons What happens to a sample of hydrogen gas (in a discharge tube) when an electric current is run through it? Electrical energy is absorbed and excites the electrons Relaxation follows H2 emits a purplish light is emitted. Color light perceived by the eyes https://youtu.be/955snB6HLB4

Bohr’s postulate #2: Electron transitions Excitation Relaxation Electron moves to higher E level lower E level Energy is Absorbed Released Form of Energy Heat, light, electrical Electro-magnetic radiation

Energy levels of the e- in the H atom can be calculated as Where E expressed in J Where E expressed in eV (R = Rydberg constant expressed in J = 2.18 x 10-18 J) n = Principal Quantum number; - Can only be integer 1, 2, 3…∞ - indicates the orbit or energy level SI unit of Rydberg constant = 1.097×107m–1 R= 2.18 x 10-18 J is actually Rx hc. Why?

Energy level in Hydrogen atom When n =1, lowest possible energy or ground state energy of a hydrogen electron = -13.6 eV Energy level in Hydrogen atom Note that because of the negative sign, E1 is the lowest in energy (instead of the highest)

Relaxation from higher orbit to Energy emitted Name of the series n=1 UV Lyman n=2 Visible Balmer n=3 IR Paschen n=4 Brackett

Multiple pathways of relaxation

Coop. Learning When E= -13.6/ n2 in eV In Joules 1eV = 1.6 x10-19 J   n=2 n=3 n=4 n=5 n=6 n= infinity

When E= -13.6/ n2 in eV In Joules 1eV = 1.6 x10-19 J n=1   E = -13.6 eV E= -13.6 x 1.6x 10-19 = 2.176x 10-18J n=2 E= -13.6/4 eV E= -5.44 x 10-19 J n=3 E= - 1.51 eV E= -2.42 x 10-19 J n=4 E= -0.85 eV E= -1.36 x 10-19 J n=5 E= -0.54 eV E= -8.70 x 10-20 J n=6 E= -0.38 eV E= -6.04 x 10-20 J n= infinity E= 0 E= 0 J

End

Why the negative sign? Because: - the energy of an electron in orbit is compared with the energy of an electron that is free from its nucleus (n=∞) This free e- has an energy = 0 - e- in orbit is more stable than e- infinitely far from nucleus, the energy of an electron in orbit is always negative. Where E expressed in J Where E expressed in eV

Multiple pathways of relaxation Q Q Atom model Energy diagram