Day 2.5A Quantum Model of the Atom
1)Two hundred years ago Dalton suggested that matter was made of atoms – indivisible particles whose mass differs from one element to another. Physicists have changed that model a great deal.
a)Just over 100 years ago J.J. Thompson proposed a plum pudding model. How was it different from Dalton’s model? Make a labelled sketch of it. What was the experimental evidence for it?
Instructions: This should be review. The students may not remember the names but they should be able to remember some models from previous chemistry or science courses. If they do this in small whiteboard groups, they can remind each other of the different bits they know. This is much more engaging for the students than listening to you teaching it. Encourage them to draw diagrams – not write words.
Electrons are stuck in positive dough. Number of electrons differs with element.
High voltages in cathode ray tubes produce identical negative particles from all elements.
This will be explored in more detail in the next unit.
b)In 1911 Rutherford proposed a solar system model. How was it different from Thompson’s model? Make a labelled sketch of it. What was the experimental evidence for it?
Electrons orbit a tiny positive nucleus. Atoms are mostly empty space.
Alpha particle scattering by gold film. This will be explored in more detail in a later unit.
Modelling Rutherford’s Model:
2) In Rutherford’s model the electron is orbiting the nucleus, like a satellite orbiting the Earth. This can be modelled with a ball rolling on a curved surface. In this model theballs/electronsare
A)not accelerating because the speed is constant
B)not accelerating because there is no net force
C)accelerating because the velocity is changing direction and there is a net force toward the centre
D)accelerating because the velocity is changing direction and there is a net force away from the centre
Instructions: The students have not studied circular motion yet. This is a conceptual introduction. The curved surface could be a funnel (I like the large oil change funnels) or stretchy fabric.
If you place the ball on the surface it accelerates toward the centre, therefore there is a net force. When the ball is in motion there will still be a net force. According to Newton’s second law, F = ma, it should be accelerating. It is accelerating because the ball is changing direction. In physics, acceleration is any change in velocity; speeding up, slowing down or changing direction.
3) The balls in this model lose energy and spiral in but the electrons in an atom do not becausethere is
A)no air resistance and no frictionB) no air resistance and negligible friction
C) negligible air resistance and no frictionD) negligible air resistance and negligible friction
Air resistance and friction are the result of contact between particles. There is nothing in the space between an electron and the nucleus.
Rutherford’s First Problem:
4)Go to Explore what you need to do to transfer energy from the electron in the transmitting antenna to the electron in the receiving antenna.The amount of energy transferred depends on the electron’s
A)positionB) speedC) velocityD) acceleration
It is easy to eliminate position. It is easiest to distinguish between acceleration and velocity if you set it to oscillate with a large amplitude and medium frequency. You can see that when it is in the middle and travelling at the greatest speed but smallest acceleration, it has a zero field. The points at the extremes where it stops but has the largest acceleration (because it is changing direction) have the greatest field.
Instructions: This electromagnetism will be covered in more detail in the next unit
5) An electron in orbit is accelerating. What is wrong with Rutherford’s model?
An orbiting object is an accelerating object. Accelerating electrons radiate energy. This energy loss means that they not be stable but should spiral into the nucleus.
6) Look at Alice and Bob: How can atoms exist? Alice’s problem. What is needed to solve it?Her problem is exactly the same as what was pointed out in question 5. She suggests that quantum ideas might help.
Rutherford’s Second Problem:
7) Look at the spectra of gases through diffraction gratings. Describe them. p. 627
Each element has a spectrum with only specific colours, therefore only specific energies.
8) The light is produced when an electron gives up some of its energy. The line spectrum is evidence that the electron can only orbit with specific energies. Go to PhET Go to one atom 30 V, single electron production, spectrometer and run in slow motion
a) Describe what happens with each electron fired. Include a diagram.
An electron is emitted by the hot element. It is accelerated by the battery.It collides with the atom and gives some of the energy to the bound electron – which is now at some higher energy level. The bound electron loses the energy by one or a series of steps – each of which emits a photon of a specific colour. . (The free electron also is accelerated some more.)
b) Describe how to produce the different colours of photons in hydrogen gas.
The four visible colours - violet, dark blue, light blue, red – are produced when the electron goes from 6, 5, 4, 3 to the second level. The uv photons are formed by drops to the first or ground level. The ir photons are formed by drops to the 3rd, 4th etc. levels.
9) Infrared light is much lower in energy than uv light. Infrared light will be given off when the electron
A)jumps to a lower energy levelB) jumps from a lower energy level
C) makes a smaller jumpD) makes a bigger jump
The energy of the photon is determined by the change in electron energy.
10) The light emitted from atoms form line - not continuous- spectra. This evidence conflicts with Rutherford’s solar system model because
A) the solar system is held together by gravity, not an electrical force
B) the solar system is much bigger than an atom
C) planets can orbit at any radius and energy, while those of electrons only have specific values
D) all of the above
The first three points are all true, but only the third one is relevant to what a line spectrum implies.
Improving Rutherford’s Model:
11) Look at PhET
a) What willthe first three models predict for spectrum of hydrogen?
Dalton’s Billiard Ball - elastic collisions, just scatters light with no change
Thompsons’ Plum Pudding - electron within nucleus is able to wobble and emits light characteristic of that energy – shown as uv, though I am not sure why that would be predicted. It’s hard to see how the electron gets its energy.
Rutherford’sSolar System– this one they should be able to predict.
b) How is Bohr’s model different from Rutherford’s? What does it fail to explain?
Bohr basically came up with a magic formula for the specific ‘orbitals’ where an electron could be. His model didn’t explain why only these orbitals were possible.It doesn’t explain why energy was not radiated while in these orbitals. It doesn’t explain how the electron can instantly jumps from one to the other. The mathematical formula only worked for hydrogen.
c)How is DeBroglie’s model similar to a standing wave?How is it an improvement over Bohr’s model?
Only certain wavelengths can fit and make a standing wave. DeBroglie’s electron waves gave a reason for why there were only certain allowed orbitals and why the transition would be sudden if not instantaneous. It even suggests why the electron does not radiate energy – it is not an orbiting particle but a standing wave.
d)How doesSchrodinger’s modeldiffer from Bohr’s? How does this model illustrate the four concepts of quantum physics? (Note: Bohr’s model only worked for hydrogen. It was replaced by Schrodinger’s model over 85 years ago. If you study chemistry, you will learn more about this than in physics.
Schrodinger replaced the physical wave with a probability wave, because there is ‘nothing’ waving. It introduced complicated math that works for all elements.
- Wave-Particle Duality: When bound, the electron acts like a wave with no definite location.
- Measurement-Disturbance: If you measure where the electron is, you will change it.
- Intrinsic Randomness: When and where an atom will emit a photon is random.
- Uncertainty: You can’t know where a bound electron is because it has no position until measured.
12) Exploring Bohr’s mathematical model.
a) The visible lines for H atoms are violet (410 nm), blue (434 nm), green (486 nm), red (656 nm). What energies do these colours correspond to in J? eV?
Instructions: Electron-volts are being introduced here as a convenient unit for tiny objects by analogy to charge. An electron has a charge of 1.602 x 10-19 C or 1 e. The violet photon has energy of 4.89 x 10-19 J or 3.05 eV. The connection of eV with volts will be reinforced in the next unit.
E = hf/e= hc/e = (6.63 x 3.00/1.60) x 10-34+8+9+19= 12.42 x 102/(nm) = 3.02, 2.86, 2.55, 1.89
b) Bohr said that only certain energy levels were allowed for the hydrogen atomand they were given by E = -13.6/n2 eV, where n = 1, 2, 3 etc. What are the first six energies in eV?
-13.6, -3.4, -1.51, -0.85, -0.54, -0.38
c) How are these energies related to the energies of the four visible colours?
They are all transition down to the second level.
3.4– 1.51 = 1.89, 3.40 - 0.850 = 2.55, 3.40 - 0.54= 2.86, 3.4 – 0.38 = 3.02
d) What other colours are predicted by this model and why don’t we see them?
The transitions to the 1st level are uv and the transitions to the 3rd and higher levels are ir.
Textbook: 12.5 p. 649 # 6, p. 660 #21-24