Please enable JavaScript.

Coggle requires JavaScript to display documents.

12 Quantum Physics (Photoelectric Effect (Laws of Photoelectric effect…

- - - - \(hf=\phi+KE_{max}\)
        
        \(\phi=hf_0=\frac{hc}{\lambda_0}\)
      - Used to release electron from metal surface
      - Remainder appears as KE of photoelectron
  - - - high frequency EM radiation has greater photon energy and thus electrons with greater energy
    - - Electron that collides with incoming photon will not receive sufficient energy, no matter how many incoming photons per unit time per unit area
    - - Photons travel at speed of light
  - - - Current changes
  - - - KE of electrons is fully countered by \(EPE=VQ\)
        
        \(\therefore \textrm{KE}_{max}=q_e\cdot V_s\)
  - - - Intensity
        \(I=\frac{nhf}{At}\)
- - - - Since \(EPE=\frac{kQq}{r}\)
        
        \(KE=\frac{k(2e)(Ze)}{d}\)
        
        \(d=\frac{k2Ze^2}{KE}\)
  - - - Rutherford Scattering
        
        As KE of alpha particle increases,
        closest distance of approach decreases
        
        \(R=R_0A^\frac{1}{3}\)
        
        Deviations
        
        Evidence for existence
        of strong nuclear force
        
        Assumption:
        Scattering ONLY caused
        by electric force
      - Diffraction
        
        Neutron :+1::skin-tone-3: because not affected by electromagnetic force
        
        Location of first minima
        
        Diffraction about circular object\(\sin\theta=\frac{\lambda}{D}\)
        
        worked example 12.15
        
        Electron :+1::skin-tone-3: because
        
        not affected by strong force
        
        has small De Broglie's wavelength → higher resolution
        
        Diameter
        \(D=\frac{\lambda}{\sin\theta}\)
        
        Radius
        \(R=\frac{D}{2}\)
        
        High energies of particle needed
        
        \(E=\frac{\rho^2}{2m}\)
        
        \(E=\frac{h^2}{2m\lambda^2}\)
        
        \(E\propto\frac{1}{\lambda^2}\)
  - - - discrete packets of energy associated with em radiation, where energy is directly proportional to frequency of radiations
      - Discrete energy levels from alpha-particles and gamma photons emitted during decay
    - - small mass --> velocity of up to 0.98c
      - mass difference converts to kinetic energy
        
        no discrete energy
        
        because of neutrino
  - - - \(A=-\frac{dN}{dt}=\lambda N\)
      - rate of disintegration
      - \(A=\lambda N_0e^{-\lambda t}\)
    - - probability per unit time that a nucleus will decay
    - - Long half-life
        
        Mass-spectrometer
- - - - \(mvr=\frac{nh}{2\pi}\)
    - - Orbital Radius
      - Quantised Energy
      - Quantised Angular Momentum
- - - - Width of barrier
      - Energy difference between
        barrier and particle
      - Mass of particle
      - \(T=e^{-2kd}\)
- - - - \(KE=\frac{p^2}{2m}\)
        
        Momentum
        \(p=mv\)
        
        Kinetic Energy
        \(KE=\frac{1}{2}mv^2\)
        
        \(p^2=2mqV\)
        
        Kinetic energy is also
        \(KE=qV\)
        
        If KE comes from EPE
        
        \(p=\sqrt{2mqV}\)
- - - - \(p=\frac{h}{\lambda}\)
- - - - \(\rho=\frac{u}{\frac{4}{3}\pi R_0^3}\)
        
        \(\rho=\frac{3u}{4\pi R_0^3}=c\)