Physics Cheat Sheet - Light And Matter x5j26

Waves – transfer of eng without the net transfer of matter Mechanical waves – Requires a medium to propagate through Wave Amplitude – maximum displacement a particle in a mechanical wave has from its origin Periodic Wave – Source of disturbance undergoes continual oscillation producing a constant wave  Light Properties – Eng, no mass, no charge   Wave Model Particle Model  Light beams cross Linear Propagation paths undisturbed Reflection  Refraction (Snell’s Law) Inverse Sq. law (I  Inverse Sq. law (I

1 D

∝

∝

)

1 2 D

)

 Linear Propagation  Diffraction Reflection– The bending of a wave around a barrier, obstacle or through a single slit Path difference (PD) – Difference in length from a point in an interference pattern to the source In phase – sources produce waves at the same freq where a crest meets a crest and a trough meets and trough Constructive Interference – addition of amplitudes arriving in phase. Coherent has constant phase difference, Destructive Interference – Crest meets a trough, amplitudes cancel Antinode – constructive interference location Node – Destructive interference location

E(J)= h(Js)∙ f(Hz) =

hc λ

 Planck’s experiments

 suggests light sources do not emit continuous waves of light by instead, discrete bundled particles of eng called photons. Planck suggested: One photon can interact with one electron at any moment Photons deliver all their eng to electron upon interaction Total eng of light beam = number of photons (n) x hf Work function (W) – minimum eng (J) required for an electron to escape from an atom (W = h fo) Threshold Freq (fo) – Minimum freq at which photoelectric  effect starts to occur (specific to different atoms) When a light of freq f is shone on an atom: h f = W + Ek  Therefore:

1 2

m(vmax)2 = h f – W

Einstein’s relationship postulated that light travelled in discrete packets of energy (quanta: hf) and defined intensity as the number of photons, rather than the  amplitude/energy of a wave If hf > W, left over eng. given off as Kinetic eng (E k) [1] Ek = hf – W [2] W = YIntercept [3] f – independent variable [4] h = gradient





Circumference of electron orbit =

Compton’s relationship:

2D w= s

Increasing D = decreasing intensity, increasing fringe spacing Diffraction

λ S

∝

- Increasing wavelength of

light used increases diffraction and hence w (fringe spacing)

λ S

≥

Swap terminals of battery (+ve terminal faces cathode) for -ve voltage at cathode (location of light) – This gives the max Ek Monochromatic used for this experiment -ve terminal towards light cathode: Accelerating voltage (voltage not impeding photocurrent) Stopping voltage – How much work done by load to stop photoelectrons from being emitted ONLY affected by freq of incident light (greater freq. = higher stopping voltage Ek =

1 2

mv2 = Stopping voltage (J)

Stopping voltage

∝

(max speed)2 of fastest electrons

(v2) Varying Intensity of incident light More intensity (Wm-2) = greater photocurrent because more photons means more electrons can be ejected every second Power output of light:

P=

ΔJ Δn h f = t t

Planck’s Constant – h = 6.63 x 10-34 Js/= 4.14 x 10-15 eV_ 1eV (1.6 x 10-19J ) – Eng gained by electron after it is moved by 1V pd [1] eV to J (× by 1.6 x 10-19J) 10-19J)

[2] J to eV (

÷

by 1.6 x 



Only applies to objects with no mass, p = momentum of photon De Broglie replaced p with mv and postulated that matter had wavelengths as well Derived relationships:

Since: EK = PHOTOELECTRIC EFFECT Photocurrent – current induced by action of light Photoelectron – electron emitted from substance illuminated by EMR -ve terminal towards cathode: Accelerating voltage (voltage not impeding photocurrent)

P=¿

h hf Energy = = λ c c

1 means significant diffraction

1 2

¿2π r

nλ (standing wave) forming a stable orbit

MATTER WAVES

Fringe spacing (w), Distance from screen (D), slit width (s)

Atoms emit specific amounts of eng to promote their electrons to excited states If an atom does not absorb enough eng to promote its electrons to the next excitation state, it retains the eng as kinetic eng for its electrons Electrons are unlikely to absorb eng in an excited state, hence eng required to promote an electron to a certain excited state is always relative to the ground level For example: 1st excitation state = 2eV, 2nd excitation state = 5ev Difference in eng levels = 3eV If an atoms 3ev, electrons will only be promoted to the 1st excitation state and retain 1ev as Ek It will NOT be promoted from the 1st excitation state to the 2nd because it is unlikely excited atoms absorb eng; even if the eng absorbed is sufficient Difference in successive eng levels becomes smaller as you move to higher eng. level (n=0 and n=1 has the greatest difference) for the dual nature of matter____________________ Discrete eng levels for particles (electrons) – Electrons moved in waves inside their eng levels (quantised) Standing waves are the eng levels electrons exist within; only certain λ of light will promote electrons (resonance)

¿

h h = mv √ 2 m E k

,

mv2

De Broglie found that the diffraction pattern of x-rays was similar to those of electrons. Hence the wavelengths of electrons (particles) was similar to those of X-Rays (waves) Spectroscopes: Emission/Absorption Spectra________________ Gas atoms absorb eng to promote their electrons to a higher eng state. As they fall back to ground level they release eng corresponding to different wavelengths of light. Electrons can emit their eng in various combinations Because absorption is a singular process and emission occurs in multiple steps there are more possible emission lines than absorption lineshas Ionisation level –eng level where an electron sufficient eng to overcome the electrostatic force binding it to the atom Spectroscope – qualitatively measures light emitted by electrons ROYGBIV. R greater wave than V, V higher freq than R Emission spectra – bright bands on a backdrop of black corresponding to the eng released by electrons falling back to ground level (electron configuration which gives the atom the most stability and least eng) Absorption spectra – dark bands in the visible spectrum due to the absorption of specific wavelength of light by an atom Atoms emit the same amount of eng they absorb

λ=

h mv

∴ n∙

h =2 π r mv

(n=1,2,3 ...) n = 1 (ground level), n=2 (1st excitation state), etc. If an integral number of wavelengths cannot fit into the circumference of electron orbit, destructive interference occurs and the orbit (wavelength) is not an eng level Left to right: n =3,4,5,6

=