Atomic Structure. AGEN-689: Advances in Food Engineering

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1 Atomic Structure AGEN-689: Advances in Food Engineering

2 Ionian scholars- 15 th century Some ancient Greek philosophers speculated that everything might be made of little chunks they called "atoms." The name comes from a Greek word meaning "uncuttable"; atoms were supposed to be unbreakable, the smallest possible units of anything Mater was made up of indivisible, invisible, incompressible, and eternal units

3 John Dalton He had noticed that elements in chemical reactions combine in certain definite proportions; This, had to mean that the elements were made of tiny, unbreakable chunks that always stick together in the same ways--two hydrogen chunks plus an oxygen chunk always makes water, for example

4 Thomson Charge Cloud Model The mass of atom is accounted for in terms of a heavy nucleus with an associated positive charge and an accompanying body of electrons The positive nuclear charge of the atom is spread out more or less uniformly throughout the structure of the atom The electrons are scattered throughout the charge space

5 Rutherford s model of the Atom Just an electron orbiting around a proton An atom is made up of electrons orbiting a nucleus in the same way that planets orbit around the sun The electrons are held in their orbits by the electric force, just as the planets are kept in theirs by gravity, and the entire atom resembles a miniature solar system. This is known as a "classical" model.

6 Rutherford s model of the Atom Announced experimental evidence showing that the Thomson s model was wrong. Rutherford's experiments consisted of shooting alpha particles at thin sheets of metal. He then measured the angles at which they came sailing.

7 Rutherford s model of the Atom Based on Thomson's model, Rutherford assumed the flying, positively charged alpha particles would be pushed a little to the side by the positive "cookie dough" in the metal atoms, and continue flying along at a slightly different angle. However, most of the alpha particles went right through the metal without changing course at all, but a few turned a full 180 degrees and went shooting back the way they'd come

8 Rutherford s model of the Atom If the positive charge were spread throughout the whole atom, as in the Thomson s model, Rutherford calculated that there would be no possibility of the particles bouncing back that way. The only way his results made sense was if he assumed that all the positive charge, and almost all the atom's mass, was concentrated in a tiny lump at the center-- what we now call the nucleus. He imagined the electrons orbiting around the nucleus like planets around the sun, with a (relatively) huge empty space between them.

9 Rutherford s atom model shortcoming Recall Maxwell s classical laws of electromagnetism: an accelerated charge emits electromagnetic radiation The orbiting electrons of Rutherford s model would emit radiation continuously They would be losing energy and no energy would be supplied (by any external force) thus spiraling inward with continuously decreasing orbital radius There's no apparent reason why an electron's orbit couldn't have just any old radius, and thus any old frequency. That flatly contradicts the experimental evidence of spectral lines

10 Bohr s model of the Atom Electrons in atoms can only be at certain energy levels, and they can give off or absorb radiation only when they jump from one level to another. If an electron falls to a lower energy level, a photon escapes; by the conservation of energy, we know that the energy of this photon is equal to the energy the electron lost--that is, the difference between the higher energy level and the lower one.

11 Bohr s Atom, cont. The electron radiates or absorbs energy when it moves from one orbital to another The energy of the photon absorbed or emitted with the orbital shift is exactly equal to the energy differential of the two orbital positions

12 Bohr s model of the Atom But we also know that the photon's energy is equal to Planck's constant times its frequency; thus, if we know what the energy levels are, we can figure out what the frequency should be.

13 Bohr s model, cont. When an atom makes a transition from one energy state, E, to a lower energy state, E1, that energy will be emitted with a quantized energy a: hf [1] E E 1

14 The angular momentum of the electron around the nucleus c f [] λ 1 1 hc ( E E ) 1 λ [3]

15 The total Energy KE+PE E 1 ( ) 1 1 v ke 1 r r 1 m v [4] m electron s mass; v velocity (at the upper and lower levels); r radius (idem)

16 Angular momentum If the electron is in a circular orbit, then: nh L mvr π [5] v L [6] mr

17 The total Energy KE+PE The total Energy KE+PE Substituting Eq.[6] into Eqn[4]: r r kze r r m L E [7] L L m e Z k E [7a]

18 To find the orbital radius We can apply Newton's second law, Fma to the electron. The force on the electron can be found using Coulomb s law: For an electron is in uniform circular motion, acceleration is Centripetal force F a kze r ke v r r [8] mv r [9] [10] Subst. Eqn[6] in [10] L r [11] kmze k8.9875x10^9 Nm/C

19 The orbital radius in fc of h Assume that an electron of mass m, charge e, and constant uniform orbit speed, v, at a radius of r from the nucleus with charge Ze, where Z is the atomic number kze r [1] mv Eliminating v from 5 and 1 n h r 4π kze m [13]simplifying r 10 n [14] Z

20 The orbital velocity By eliminating r between Eqns [5] and [1]: v kze π nh Z n [15]

21 KE, PE & KE, PE & En (sum) (sum) 4 1 h n m e Z k mv KE π [16] 4 4 h n m e Z k r kze PE π [17] 4 h n m e Z k E n π [18]

22 Bohr s Formula: Lnh nh/π Bohr found that his theory agreed precisely with this formula if he assumed that an electron's angular momentum was restricted to a certain set of values Given the angular momentum, Bohr could easily find the electron's speed and orbital radius, which would allow him to calculate its kinetic and potential energy. This in turn meant that the difference in energy between any two orbits could be found, so the frequency of he corresponding photon could be calculated

23 Bohr s model E n π k n Z h e 4 m The angular momentum had to be an integer multiple of h/π; A value of n1 corresponds to the ground state, where the electron possesses its lowest possible energy. As n grows larger, the difference between consecutive energy levels becomes smaller and smaller; in fact, it approaches zero as n approaches infinity

24 Questions about Bohr s ideas Why should an electron s angular momentum have only certain values? Why the electrons emit or absorb radiation only when they jump between energy levels?

25 The wave nature of matter Louis de Broglie came up with a fascinating idea to explain them: matter, he suggested, actually consists of waves. it gives a very nice reason why an electron can only be in certain orbits. He assumed that any particle--an electron, an atom, -had a "wavelength" that was equal to Planck's constant divided by its momentum

26 Photon momentum P λ E hf c c h mv h λ h e( KE ) m de Broglie knew that the momentum and wavelength of a photon actually were related in just this way Electromagnetic radiation could have the ppt of waves and particles

27 Broglie s atom Instead of having a little particle whizzing around the nucleus in a circular path, it has a wave sort of strung out around the whole circle. Now, the only way such a wave could exist is if a whole number of its wavelengths fit exactly around the circle. If the circumference is exactly as long as two wavelengths, say, or three or four or five, that's great, but two and a half won't cut it

28 Broglie s idea If electrons are waves, they don't give off or absorb photons unless they change energy levels. If it stays in the same energy level, the wave isn't really orbiting or "vibrating" the way an electron does in Rutherford's model, so there's no reason for it to emit any radiation. If it drops to a lower energy level... let's see, the wavelength would be longer, which means the frequency would decrease, so the electron would have less energy. Then it makes sense that the extra energy would have to go someplace, so it would escape as a photon--and the opposite would happen if a photon came in with the right amount of energy to bump the electron up to a higher level.

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