Tag: physics

Emission Spectra: How Atoms Emit and Absorb Light

Emission and absorption spectrum of Hydrogen. Image adapted from the one by Wikimedia Commons User:Adrignola.

When a photon of light hits an atom three things can happen: it can bounce off; it can pass through as if nothing had happened; or it be absorbed. Which one happens depends on the energy of the light, and which atom it is hitting. Hydrogen will absorb different energies from helium.

The interesting thing is that each atom will only absorb photons with exactly the right energy. You see, when the light hits the atom, the atom will only absorb it if it can use it to bump an electron up an electron shell.

An oxygen atom with two electrons in the innermost shell and six in the second shell.

An oxygen atom, for example, has eight electrons, but these fit into two different electron shells. The innermost shell can only hold two electrons, so the other six go into the second shell (which can take a maximum of 8). This is the “ground state” of the atom, because it takes the least amount of energy to keep the electrons in place.

However, if the atom gets hit by just enough energy, one of the electrons can be bumped up into a higher shell. The atom will be “excited” and “want” the electron to drop back down to the lower shell.

And when the electron drops back, it will release the exact same amount of energy that it took to move it up a shell in the first place.

A hydrogen atom's electron is bumped up an energy level/shell by ultraviolet light, but releases that light when the electron drops back down to its original shell.

For hydrogen, the energy to bump up an electron from its first to its second electron shell comes only from light with a wavelength of 1216 x 10-10m (see here for how to calculate). This is in the ultraviolet range, which we can’t see with the naked eye.

However, the energy absorbed and released when the electron moves between the second and fourth shells is 6564 x 10-10m, which is in the visible range. In fact, it’s the red line on the right side of the emission spectrum shown at the top of the page.

The visible part of the emission spectrum of hydrogen and its corresponding electron shell jumps. Note that different colors of light have different energies, and that the blue light is more energetic (and has a shorter wavelength) than red light.

Since this emission signature is unique for each element, looking at the colors of other stars, or the tops of the atmospheres of other planets, is a good way of identifying the elements in them. You can also do flame tests to identify different elements.

Copper.
Lithium.
Sodium.

The University of Oregon has an excellent little Flash application that shows the absorption spectrum of most of the elements in the periodic table (NOTE that the wavelengths they give are in Angstroms (Å) which are 1×10-10m; or tenths of a nanometer (nm)).

Interactive app that shows the absorption spectrum of the elements in the periodic table. From the University of Oregon. Wavelengths are in Angstroms (Å), and 1 Å = 0.1 nm.

Equations

The wavelength of light emitted for the movement of an electron between the electron shells of a hydrogen atom is given by the Rydberg formula:

\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)

where:
\lambda = wavelength of the light in a vacuum
R = Rydberg constant (1.1×107 m-1)
n_1 and n_2 are the electron shell numbers (the innermost shell is 1, the next shell is 2 etc.)

— see an example calculation here.

The amount of energy that corresponds to a particular wavelength of light is given by:

E = \frac{hc}{\lambda}

where:
E = Energy (J),
\lambda = wavelength of the light in a vacuum (m),
h = 6.6×10-34 Js,
c = speed of light in a vacuum (3×108 m/s).

— via Wikipedia.

References

The National Institute of Standards and Technology (NIST) has more extensive emission spectra data.

Parabolic Mirrors

Parabolic mirrors magnify by reflecting parallel rays of incoming light onto a single point. (Adapted from Wikimedia Commons User:Nargopolis).

We’re talking about light and sound waves in physics at the moment, and NPR’s Morning Edition just had a great article on how the enormous, ultra-precise, mirrors that are used in large telescopes are made.

Astronomical observatories tend to use mirrors instead of lenses in their telescopes, largely because if you make lenses too big they tend to sag in the middle, while you can support a mirror all across the back, and because you have to make a lens perfect all the way through for it to work correctly, but only have to make one perfect surface for a parabolic mirror.

ScienceClarified has a great summary of the history of the Hubble Space telescope, that includes all the trouble NASA went through trying to fix it when they realized it was not quite perfect.

Large parabolic mirrors are used for magnification in telescopes. (Image via Wikipedia).

In addition, it’s interesting to note that you can also make a parabolic surface on a liquid by spinning it, resulting in liquid telescope mirrors .

How Long does it Take to Make a Vpython Program?

Moving the magnet through a wire coil creates an electric current in the wire. Animation captured from the VPython program: Magnetic Induction - Coils.

My students asked me this question the other day, and while slapping together an animation of electromagnetic induction I gave it some thought.

This program itself is really simple. It took about 15 minutes.

But that’s not counting the half hour I spent searching the web for an image I could use to illustrate magnetic induction and not finding one I could use.

Nor does it count the four hours I spent after I got the animation working to get the program to take screen captures automatically. Of course, I must admit that figuring out the screen captures would have gone a lot quicker if I’d not had to rebuild all my permissions on my hard drive (I’d recently reformatted it), and reinstall ImageMagick and gifsicle to take the screen captures and make animations.

Solar Flare

Just in time for our physics test — on electromagnetism — the Sun has had a Coronal Mass Ejection of charged particles that is heading toward the Earth.

[The Coronal Mass Ejection] is moving at almost 1,400 miles per second, and could reach Earth’s magnetosphere – the magnetic envelope that surrounds Earth — as early as tomorrow, Jan 24 at 9 AM ET (plus or minus 7 hours). This has the potential to provide good auroral displays, possibly at lower latitudes than normal.

— Fox, 2012: M8.7 Solar Flare and Earth Directed CME from NASA.

The Earth's magnetic field deflects charged particles around the planet, although some do get redirected down toward the poles, making the arouras. (Image from NASA's Spaceplace).

A Coronal Mass Ejection has about 100 billion tons of electrons, protons and other particles (NASA Cosmicopia, 2011), usually ionized, that would bombard the Earth and the atmosphere if we weren’t protected by the Earth’s magnetic field.

Most of the ions are deflected around the Earth but some get focused down toward the poles. At the poles, these ions hit nitrogen and oxygen molecules (that make up 98% of the atmosphere), exciting many of them. Excited atoms and molecules give off light. The light shows created are called the auroras.

Aroura australis, as seen from the International Space Station.

I like the second video they post because, at the end, there is a splatter of interference from all the charged particles affecting the detector.

Making Motors

A simple electric motor.

Our exercise in building simple electric motors was quite a success.

Students enjoyed doing it, even though it was challenging making the coil just right so it would spin easily. They persisted and enjoyed that wonderful eureka moment when it actually worked.

Motor Speed

One group wanted to figure out how fast the armature was spinning. Because of small imperfections inherent to hand-made parts, we found that the armatures would bounce, ever so slightly, with each rotation. So the students recorded the sound using their laptop, and then counted rotations off the recorded sound wave. I think they came up with about 10 rotations per second.

I need to check if there’s a free phone app we can use that will show the sound waveform more efficiently — Pocket WavePad seems like it might work.

Accidental arc welding

At the end, some students wanted to figure out just how fast they could get the motor running. Disdaining the online instructions, they went for more power, hooking up all the batteries they could scavenge from the other groups before I had to make them stop. They did manage to weld the insulating varnish on the coil wire to the paperclip contact before the end.

All the sparks did lead to a discussion of how arc welding works, however, which I was able to tie into the maths of transformers; cheaper arc welders (like this one) take in 20 Amps at 120 Volts, and output 70 Amps at 22 Volts.

This group did not want to stop, so I gave them permission to pass on P.E. for that one day, with a note that said they were doing some “remedial” physics. They got a kick out of that.

Diagram showing the parts of a simple motor.

Generating Electricity

Magnetic fields and electric fields are directly related:

  • We saw before that a current moving through a wire creates a magnetic field.*
  • The opposite is also true. A moving magnetic field induces an electric field (and thus a current) in a wire (from Faraday’s Law).

Electromagnetic Induction

Moving a magnet through a wire coil creates an electric current. The faster you move the magnet, or the more coils of wire you have, the greater the current. Moving the magnet back and forth will switch the direction of the current back and forth as well, creating an alternating current.

So, simply moving a magnet next to a wire, or through a coil of wire, will induce a voltage in the wire.

You can create more voltage by:

  • Faster motion.
  • More coils of wire.

Notes:

Relative Motion: moving the coil of wire around the magnet would create the same voltage as moving the magnet through the coil.

Moving the magnet creates the same current as moving the coil.
Moving the coil creates the same current as moving the magnet.

Conservation of Energy: By moving the magnet, you convert the kinetic energy of the motion to electrical energy.

  • So the greater the voltage you want to create, the more energy it will take to move the magnet. If you have a lot of coils and are creating a large voltage, the magnet is going to be harder to push through the coil because the induced electrical field induces a magnetic field that opposes the original magnet.

Current Direction: Moving the magnet back and forth will switch the direction of the current back and forth as well, creating an alternating current.

Faraday’s Law (37.2)

The voltage induced in a coil depends on the number of loops and the rate at which the magnetic field changes (as well as the resistance of the coil material — better conductors will permit a greater voltage).

Electrical Generators

Diagram showing the parts of a simple motor.

If we make a coil like the ones we used to make the motors, but took out the battery from the circuit then the motor would not move. However, if we rotated the coil ourselves, mechanically, as it sat over the magnetic field, we would create a current in the wire. This is how generators create electricity.

Generators (mostly) create electrical currents by rotating wire coils inside magnetic fields.

Alternating Current Generators

A generator adapted from our motor would only have a current as long as the copper wire from the exposed side of the coil was completing the circuit. When the insulated side was touching the paperclip there would be no current. Electrical power plants are set up so that the rotating coil (also called an armature) is always in electrical contact, but when the coil goes through the second half of its rotation the current is reversed in direction. This switching back and forth of the direction of the current in the wires is how alternating currents are created.

Power Plants

Electrical power plants turn their wire coils (armatures) in any number of ways.

  • Wind turbines and hydroelectric turbines use wind and water respectively to spin their wire coils directly.
    • Hydroelectric power plant diagram. Via the USGS.
  • Most other power plants produce heat energy to boil water, which creates steam, which is piped past the turbines that turn the coils.
    • Coal, oil and natural gas plants burn these fossil fuels to produce the heat;
    • nuclear power plants use the heat generated from radioactive decay to produce the steam that turns the turbines;
      • Diagram of a nuclear power plant. Image via the TVA.
    • on the other hand, solar panels don’t use turbines or any moving parts to produce electricity.

Motors versus Generators (37.4)

Motors and generators are essentially the same, except that motors use electricity to produce mechanical energy, while generators use mechanical energy to produce electricity.

Notes

* edited March 22nd, 2012 at 10:01 pm, in response to feedback in this comment.

Electromagnets

Electric Currents Generate Magnetic Fields (36.5)

An electric current in a wire creates a magnetic field around the wire. Image adapted from Wikimedia Commons User:Stannard.

Moving charges create magnetic fields. Currents moving through a wire are moving electric charges (electrons). Therefore, current-carrying wires generate a magnetic field around them.

Bending wires into a loop will create will create a magnetic field through the loop.

  • The more loops you have the stronger the magnetic field.
  • The magnets created by pushing a current through loops of wire is called an electromagnet.
  • If you use superconducting wire, you can create an extremely powerful superconducting magnet that can be used in magnetic levitation (maglev) trains.
Magnetic field through a coil of wire (with a current running through it). The more loops of the wire, the stronger the electric field.

Magnets Deflect the Movement of Charged Particles (36.6)

Moving charged particles create magnetic fields. So if a moving charged particle encounters a magnetic field the two magnetic fields will interact and the motion of the particle will be deflected.

A charged particle is deflected from it's forward motion when a magnetic field is turned on.

Note that the deflection only occurs when the particle is not traveling parallel to the magnetic field lines.

  • The big, old styled TV’s use this to shoot electrons at the screen to make the picture.
  • The Earth’s magnetic field deflects the charged particles ejected by the Sun, protecting the planet.
The Earth's magnetic field protects us from the solar wind. Image from NASA.

Interaction Between Magnets and Currents in Wires

Just like charged particles are deflected when they run into a magnetic field, charges running through a wire will create a magnetic field that will interact with external magnets to cause the wire to move.

  • The force on the wire is perpendicular both to the direction of the current and the lines of the magnetic field.
  • If you reverse the current in the wire (send it the other way) the force will be in the opposite direction.
The force resulting from a current is at right angles to the magnetic field and the current; the "right hand rule" is an easy way to remember this. Image adapted from User:Acdx on Wikimedia Commons.

You can use this principle to create a galvanometer, which is a device that detects electric currents, or to build motors.

A simple electric motor.

Earth’s Magnetic Field

Convection currents in the Earth’s molten, metalic outer core create the Earth’s magnetic field.

Because the pattern of convection changes over time, the Earth’s magnetic field:

  • Is not located at the north pole (axis of rotation).
  • Wanders: it moves a little each year.
  • Flips so its poles reverse every 800,000 years or so.
The location of the magnetic north pole changes with time. Image via the National Forest Service.

As lava cools, the magnetic minerals in it orient themselves with the Earth’s magnetic field. One way of telling how old basalt rocks on the seafloor are is by looking at the direction of their magnetic field. Since the Africa and the Americas are moving apart, slowly over millions of years, there is a suture in the Earth’s crust in the middle of the Atlantic ocean where new seafloor is made from erupting, under-sea volcanos. As a result, there are magnetic stripes all along the Atlantic Ocean (and all the other oceans too) that have recorded each time the Earth’s magnetic polarity has reversed.

Magnetic striping in oceanic crust. Image from the USGS.

The USGS has high-resolution geomagnetic maps.

Map of the remnent magnetism in the crust (focus on North America and North Atlantic). Via the USGS.

Gravity, the Electromagnetic Forces, and the Inverse Square Law

Calculating the forces between two charged particles (electric force), two magnets (the magnetic force), and two masses (the gravitational force) require remarkably similar equations. But, while electricity and magnetism are directly related (that’s why it’s called electromagnetism), gravity is its own fundamental force. Yet they all depend (inversely) on the square of the distance between the two objects creating the force, so they’re all said to obey some form of the inverse square law.

Gravitational Force (Fg)

The force exerted by two masses on one another is:

F_g = G \frac{m_1 m_2}{d^2}

where:

  • G is the gravitational constant (6.67300 × 10-11 m3 kg-1 s-2
  • m1 and m2 are the masses of the two objects attracting one another.
  • d is the distance between the two objects.

Electrical Force (Fe)

The force exerted by two electrically charged objects on one another (like a proton and an electron), is:

F_e = K \frac{q_1 q_2}{d^2}

where:

  • K is the electrical constant, sometimes called Coulumn’s constant (8.9876 × 109 N m2 C-2
  • q1 and q2 are the sizes of the charges (in Coulumbs) of the two objects attracting one another.
  • d is the distance between the two objects.

Magnetic Force (Fm)

The force exerted by two magnets on one another, is:

F_m = \mu \frac{p_1 p_2}{d^2}

where:

  • μ is a constant, (a little simplified)
  • p1 and p2 are strengths of the magnetic poles of the two objects attracting one another.
  • d is the distance between the two objects.

The magnetic force is a little more difficult to give a single equation for, because you need to factor in the shape of the magnets.

Inverse Square Laws

In addition to gravity, electric, and magnetic forces, light (which is electromagnetic radiation) and sound also obey inverse square laws.