Atoms and Energies

But first, a synopsis of storage

Dyd

Optical Storage Light shining through an opening spreads

and produces diffraction patterns Light traveling through a circular opening

produces a circular pattern, such as the one shown below

y

tan = y/D

d sin = 1.22

More Optical Storage Laser light is focused through a (circular) lens

onto the surface of a CD The central max of the diffraction pattern must be

no larger than one bit if data is to be resolved The diameter d of the lens, the distance D between

the CD and the surface (which should be the focal length of the lens, and the wavelength of light all affect the size of the central maximum

The ratio D/d for a lens is constrained to be >1 by practical manufacturing considerations

Final Optical Storage Remarks Bits are written as lands or pits on a disk Light striking a (smooth) land undergoes total

reflection toward the detector This is a 1

Light striking a (rough) pit undergoes diffuse reflection so the detector receives a much smaller amount of light and doesn’t trigger This is a 0

Electrical Storage The electric force FE on a charge q0 can be considered due

to an electric field which is produced by other charges qi in the area

FE = q0 E If the charge is positive, the force points in the same

direction as the field If the charge is negative, the force points in the opposite

direction as the field Electric fields, then, point from positive charges toward

negative charges, or from high “potential” to low potential

More Electrical Storage We can draw field lines using two guidelines:

Electric field lines point in the direction of the field The spacing of the field lines represents the

strength of the field (Closer spacing means stronger field)

If moving a charge between two points requires work (or does work), the charge gains (or loses) potential energy:

U = –W = – F dx = – q0 E dxV = – E dx

Still More Electrical Storage An electric field can be “stored” using two oppositely-

charged plates, an arrangement called a capacitor Capacitors storing charge Q will maintain a potential

difference, or voltage V, between the plates that is proportional to Q:

Q = CV Capacitance C is independent of V and Q and depends only

on geometry and materials of device:

C = 0 A/d,

Where A is the area of each parallel plate, and d is the spacing between the two plates

Final Electrical Storage Remarks

Capacitors are used in RAM: A charged capacitor is a 1 An uncharged capacitor is a 0

Reading a capacitor discharges it, so you must continually re-write when reading

Capacitors lose charge over time (charge will slowly leak into air or other insulator), so capacitors are not good for long-term storage

Magnetic Storage The smallest region with uniform magnetism is

called a “domain” Each bit requires two domains to allow for error

identification If two domains are magnetized in same direction,

the bit is a 0 If two domains are magnetized in opposite

directions, the bit is a 1 Direction of magnetization must change at the

start of each new bit.

Magnetic Storage: Writing Magnetic fields have two sources:

Currents (electromagnetism) Alignment of intrinsic “spin” of particles

(ferromagnetism) Magnetic data is written by running a current

through a loop of wire near the disk resulting magnetic field aligns spins in region of

disk and produces magnetic domain switching current produces magnetic domain with

magnetism in opposite direction

A changing magnetic field induces a current in a coil of wire proportional to the derivative (rate of change) of the field

The field, emf, and current also depend upon the area A of the loop, and the number of turns in a coil.

This is summarized in Faraday’s Law:

Magnetic Storage: Faraday’s Law

dt

dBA

dt

diR B

BAdABB

Magnetic Storage: Reading by Induced Currents

As magnetic data passes by coil of wire, changing field induces currents increase in field (more positive or less

negative) induces current in opposite direction of that induced by a decrease in field (more negative or less positive)

Number of changes in a bit indicates whether bit is 0 or 1

Magnetic Storage: Reading by Magnetoresistance Charges traveling through magnetic field experience

magnetic force (provided velocity and field are not aligned):

FB = qv x B Force is perpendicular to velocity (and to field), so charges

are pushed “off track”, resulting in more frequent collisions and thus an increased resistance

Current through a loop of wire near magnetic data will vary as magnetic field does, giving a very sensitive indication of magnetic data

Magnetic Storage: Reading by Giant Magnetoresistance Giant Magnetoresistance (GMR) is a completely

different effect from Magnetoresistance (MR) Both utilize magnetic data’s effect on resistance,

but that’s the only similarity MR is the regular “Lorenz” force on charges

moving in a magnetic field GMR exploits spin-dependent scattering and

requires very carefully-crafted devices such as spin valves

Giant magnetoresistance

When magnetic field is present in magnetic superlattice, scattering of electrons is cut dramatically, greatly decreasing resistance

Superlattices are hard to mass-produce, but the effect has been seen in three-layer devices called “spin valves”

The origin of giant magnetoresistance is very different from that of regular magnetoresistance!

On To Atoms Around the turn of the century, Bohr proposed that

electrons in atoms can only occupy certain, quantized energy “states”

When an electron moves from one allowed state to another, it needs to absorb or emit a particular amount of energy Often that energy takes the form of light Only specific energies (and therefore wavelengths) of light

will be emitted by a particular element The collection of energies emitted or absorbed by an

element is called the atomic spectrum of that element

Do Today’s Activity

Our Model of the Atom

If the atom is in the “ground state” of lowest energy, electrons fill the states in the lowest available energy levels. The first shell has two possible states, and the second shell has eight possible states. Higher shells have more states, but we’ll represent them with the eight states in the first two sub-shells.

Electrons in the outermost shell are called “valence” electrons. We’ll

make them green to distinguish from e- in filled shells

E=0 (unbound)

n=1

n=2n=3n=4

Really eight closely spaced energies, since no two electrons can occupy same state

The Hydrogen Atom Has one electron, normally in the ground state n=1 This electron can absorb energy and go to a higher state, like n=3 The atom will eventually return to its ground state, and the electron

will emit the extra energy in the form of light. This light will have energy E = (13.6 ev)(1/1 – 1/32) = 12.1 eV The corresponding wavelength is = hc/E = 1020 Å

E=0 (unbound)

n=1

n=2

n=3n=4

Other Atoms Electrons can absorb energy and move to a higher level

White light (all colors combined) passing through a gas will come out missing certain wavelengths (absorption spectrum)

Electrons can emit light and move to a lower level Calculating the allowed energies extremely complicated for anything

with more than one electron But can deduce allowed energies from light that is emitted

E=0 (unbound)

n=1

n=2

n=3n=4

Really eight closely spaced energies, since no two electrons can occupy same state

Stuff to remember about Spectra ENERGY IS QUANTIZED Different elements have different allowed energies (since

different numbers of protons and electrons provide different structure of attraction

Light emitted when electrons move from a high energy level to a lower energy level in an atom will have only certain, QUANTIZED, allowed energies and wavelengths.

Those wavelengths depend solely on the element emitting the light and compose the characteristic emission spectrum for that element