Electromagnetic Radiation and Quantum Phenomena

Electromagnetic Radiation and Quantum Phenomena

1. Photoelectric effect

   • Radiation with a high enough frequency onto the surface metal will emit electrons
     • Metals contain free electrons
       • Free electrons absorb the radiation and vibrate if it absorbs enough energy the bonds can break and the electrons are released they are called photoelectrons
         • Thus energy needed to break the bonds is called the work function and value varies depending on the metal
           • F1= ∅/h
             • F1= Frequency threshold
             • ∅= work funchtion
             • h= Planck's constant
           • If energy is higher than the work function than it is converted into kinetic energy
             • Max kinetic energy Ek=hf-∅
               • Kinetic energies of photoelectrons can vary as they experience different loss of energy
                 • Stopping potential also used to work out the max kinetic
                   • To stop electron need to do work against the applied potential difference this is the energy needed to stop the fastest moving photoelectron (travelling with the max kinetic energy)
                     • Work done by potential difference= energy of photoelectron
                       • eV=Ek
                         • e= charge of electron
                         • V= stopping potential
                         • Ek= max kinetic energy
                 • The minimum amount of enrgy that can be lost is equal to the work function (∅) hence we can work out the max amount of kinetic energy
               • Derive this- Ek=1/2mv^2
                 • Derive the photoelectric equation hf= ∅ + 1/2mv^2
   • Conclusions
     • 1- If the frequency is below the frequency threshold the no photoelectrons are emitted
       • Wave theory cannot explain threshold frequency
       • Wave theory energy proportional to intensity as all electrons on the metal surface gain some energy eventually gaining enough to escape
     • 2-Photoelectrons are emitted with a variety of kinetic energies, the max kinetic energy will increase the frequency
     • 3- Intensity is the amount of energy hitting the plate per second, the max kinetic energy is not affected by intensity
     • 4- Photoelectrons emitted per second (and the energy they carry) are proportional to the intensity
       • If the number of photelectrons increase so does intensity and vice versa
       • If the intensity increases the number of photoelectrons increases and vice versa
       • Kinetic energy increases as the amount of energy does
   • Photons
     • EM waves released in discrete packets or quanta
     • E=hf=hc/λ
       • E= Energy of photon
       • h= planck's constant
       • c= Speed of light
       • λ= wave length

2. Energy levels

   • ground state- Lowest energy level of atom or electron in atom
   • Excited state- Any state above the ground level is considered to be excited
   • Ev unit used to describe the energy carried by an electron after acceleration with a potential difference of 1
     • Conversion eV to J 1eV= 1.6 x 10^-19 J
       • J to eV >> divide
       • eV to J >> multiply
   • transitions
     • Moving down a level releases a photon
       • The energy of this photon is equal to the difference between the the two levels of transition
       • Ionisation requires the atom to surpass the ground state this is known as ionisation energy
     • Moving up a level is known as excitation
     • Change in E (J)= E1 -E2 = hf
       • Derive Change in E(j)= hc/λ
   • Photon emission- fluorescent
     • Use excitation of electrons and photons to create visible light
       • 1. Mercury (Hg) with high voltage across
         • 2. Voltage accelerates free electrons which ionise mercury atoms producing more electrons
           • 3. The increased amount of electrons means the chance of collision between the electrons and mercury atoms is more likely cause them to move up energy levels
             • 4. They come back to the ground state releasing photons in the UV range, the photons have a range of energies and wavelengths based on the different electron transitions
               • 5. The phosphorus coating absorbs the photons exciting the electrons to higher levels then lose photons of visible light as they cascade down the levels

3. Spectra

   • Line emission
     • Gratings- diffract light of different wavelengths at different angles, creates more defined spectral lines than prisim
     • Black background with bright lines which correspond to different wavelengths
     • Evidence electrons have energy levels as it moves down the photons produced are equal to the difference in energy levels, and correspond to specific wavelengths and line spectrum
   • Line absorption
     • Continuous spectra- White light and hot objects, in the infrared and visible spectrum, emit continuous spectra as electrons are not confined to energy levels or bound to atoms
     • Occurs when light with continuous spectrum passes through cool gas
       • Low temperatures mean electrons more likely a ground state
         • photons at correct wavelength are absorbed causing excitation hence these wavelengths are missing from the continuous spectrum
   • Compaeison

4. Wave particle duality De Broglie- The evidence

   • Diffraction
     • Spreading out of waves
     • Varies depending on the size of gap and size of the wave
       • Bigger the wave and smaller the gap= more diffraction
       • Smaller the wave bigger the gap= less difraction
   • Photoelectric effect
     • Particles (photons)
     • Interact with electrons
   • Electron diffraction shows that electrons have wave like properties
     • Electron microscopes
     • Electrons accelerated in a vaccum passing through graphite crystal, they diffract like passing through a slit creating patterns/rings
       • Slower electrons create larger rings similar to varying wavelengths and faster electrons had smaller (concise) rings
   • Relates wavelength to moving particle (momentum = mass x velocity)
     • Hence λ= h/mv