Unit 5 - Waves

Question 1

Traveling Waves

Answer 1

• A = amplitude
• Amax = max amplitude
• Amin = min amplitude
• waves propagate through space and time
• crests = top
• troughs = bottom

Question 2

Wavelength

Answer 2

λ (lambda) = the distance from crest to crest or trough to trough

Question 3

Velocity of Waves

Answer 3

v = distance/time

only for traveling waves
memorize

Question 4

Frequency

Answer 4

• slanted v (nu)
• number of crests or troughs that pass a stationary point in space per second

Question 5

Relationship Between Wavelength, Frequency, and Velocity

Answer 5

v = λ * slanted v (nu)

Question 6

speed of light

Answer 6

3.0 * 10^8 m/s

Question 7

photons

Answer 7

• particle nature of light
• stream or energy particles whose energy is dependent on the frequency

Question 8

Planck’s Constant

Answer 8

h = 6.26 * 10^-34 J*s

Question 9

Energy of Photons

Answer 9

Eph = h * slanted v (nu) = h * C/λ

memorize

Question 10

Early Model of an Atom: J.J. Thompson

Answer 10

• 1807 J.J. Thompson
• atoms of all elements contain identical negatively charged particles
• plum pudding model: atom has diffuse matrix of positive charge and electrons are embedded within that matter

Question 11

Early Model of an Atom: Ernest Rutherford

Answer 11

• 1909 Ernest Rutherford
• alpha particle scattering experiment
• Alpha particles (positively charged, emitted from a radioactive source) were directed at the foil
• A thin sheet of gold foil was used
• Most alpha particles passed straight through the foil with little or no deflection
• A small fraction of particles were deflected at large angles
• An extremely tiny number even bounced back toward the source

Conclusions:
- Atoms are mostly empty space, allowing most alpha particles to pass through
- There is a small, dense, positively charged nucleus at the center of the atom that causes large deflections
- The plum pudding model was incorrect; electrons orbit a central nucleus rather than being embedded in a diffuse positive cloud

Question 12

Early Model of an Atom: Planetary Model

Answer 12

• 1911 Planetary Model
• Nuclear model of the atom
• All of the positive charges and most of the mass are confined in a tiny nucleus that is 4 orders of magnitude smaller than the size of an atom
• electron follows a planetary like orbit

Question 13

Early Model of an Atom: Niels Bohr

Answer 13

• 1913: Bohr Model
• It only works for H atoms and H-like ions (one electron ions)
• this is because having multiple electrons will complicate the orbits with electron-electron repulsion
• Incorporates the idea of energy quantification into the classical mechanics description of the atom
• only certain energy levels and discrete orbits are allowed

Question 14

Energy of an Orbit

Answer 14

• for one electron

En = - 2.18 * 10^-18 J * (z^2)/(n^2) = -13.6 eV * (z^2)/(n^2)

• Rydberg Constant: 2.18 * 10^-18
• Z = atomic number of the atom or ion
• J = joule, unit of energy
• eV: electrons volt, unit of energy
• as n increases, En becomes less negative and the spacing between the energy levels will decrease due to En being proportional to -1/n^2

Question 15

Radius for Each Allowed Discrete Orbit

Answer 15

• r = n^2/z * a0
• a0 = 52.9 pm = 0.529 Å = 5.29 * 10^-11 m
• 1pm = 1^-12 m
• 1 Å = 10^-10 m
• as n increases, the radius increases, spacing between orbits increases due to r being proportional to n^2

Question 16

Angstrom Conversion

Answer 16

1 Å = 10^-10 m

memorize

Question 17

How to do Energy State Diagram

Answer 17

Step 1: Draw the Vertical Axis
- Label it Energy (E).
- Higher on the diagram = higher energy level.

Step 2: Draw Horizontal Lines
- Each line represents an energy state (energy level):
- E1 = (ground state), n = 1
- E2, E3, E4, … = (excited states), n = 2,3,4,…
- E = 0 means e- is not confined in the atom

Step 3:
- draw arrows up or down
- up = photon absorption
- down = photon emission

Question 18

Photon Absorption

Answer 18

Eph = h * nu = h *C/λ =|ΔE| = |Ei - Ef|

memorize

Question 19

Electrons Waves

Answer 19

• 3D standing waves that are confined around in a single point, the nucleus
• fixed time
• spherical
• electron waves in an atom do not have hard boundaries and can spread out
• not completely confined in the atom
• signs of amplitude of e- change in time
• Every e- in an atom is described by a wave called orbitals
• e-‘s do not follow orbits

For one sphere:
- A is all + or all -
- Pure crest or trough wave
nucleus in the center

For two spheres:
- crest and trough lobe
- A is + or - in each lobe
- tangent to the nucleus

Question 20

Standing Waves

Answer 20

• Oscillate like violin strings
• Has boundary conditions
• Crests and troughs are at fixed positions
• at node, string remains motionles at all times
• # nodes = n - 1memorize
• signs of amplitude change when you cross the nodes
• each standing wave has a different energy
• A must be 0 boundaries or it is not a standing wave

Question 21

Image Resolution

Answer 21

• image resolution is the amount of detail an image conveys
• the resolution of an image is never better than the wavelength of the electromagnetic radiation used
• aka if the wavelength if longer (due to lower frequency) then the image will be more blurry
• shorter wavelengths result in better resolution
• therefore want highest freqency for best resolution (λ = v/nu)

Question 22

Things to Remember

Answer 22

1. If it asks “how long/how much time” you probably use v = distance/time using C as the speed
2. If it asks for the wavelength you probably use λ = v/nu
3. If it asks for the wavelength given n values you probably use|ΔE| = |Ei - Ef| and then use Eph = h *C/λ
4. ΔE is the energy of the photon and it must match the energy difference of the states you are going to and from. If the photon has too little energy, the electron can’t reach the higher state. If the photon has too much energy, the electron can’t absorb it either.
5. around 1 nanometer (1 x 10⁻⁹ m) to 400 nanometers (4 x 10⁻⁷ m) is ultraviolet radiation

Question 23

Electromagnetic (EM) Spectrum

Answer 23

• shorter wavelength = higher energy

Highest Energy to Lowest Energy (left to right on the spectrum):

1. Gamma rays (shortest wavelength, highest energy)
2. X-rays
3. Ultraviolet (UV)
4. Visible light (violet → red)
5. Infrared (IR)
6. Microwaves
7. Radio waves (longest wavelength, lowest energy)

This is because E = (h*c)/λ

Question 24

Heisenberg Uncertainty Principle

Answer 24

you cannot simultaneously know both the exact position and momentum of a particle