Dual Nature of Radiation and Matter — MHT-CET Physics

Formulas (4)

• What Intensity and Frequency Each Control · Threshold
  $$h\nu_0 = \phi = \frac{hc}{\lambda_0}$$
• Einstein's Equation in One Situation · Einstein's equation
  $$h\nu = \phi + \tfrac{1}{2}mv_{\max}^2 = \phi + eV_0$$
• Threshold From Two Readings · Two readings
  $$e(V_1 - V_2) = hc\left(\frac{1}{\lambda_1} - \frac{1}{\lambda_2}\right), \qquad \lambda_0 = \frac{hc}{\phi}$$
• Reading the Photoelectric Graphs · Stopping-potential line
  $$V_0 = \frac{h}{e}\nu - \frac{\phi}{e}$$

Watch out for (7)

• Letting intensity change the stopping potential
  → What Intensity and Frequency Each Control
• Saying doubled frequency doubles the kinetic energy
  → What Intensity and Frequency Each Control
• Taking the speed ratio from the photon energies
  → Einstein's Equation in One Situation
• Scaling the work function with the frequency
  → Einstein's Equation in One Situation
• Dividing the two equations directly
  → Threshold From Two Readings
• Swapping λ₁ and λ₂ in the answer
  → Threshold From Two Readings
• Reading intensity from the cut-off
  → Reading the Photoelectric Graphs

Formulas (3)

• Wavelength, Momentum and Kinetic Energy · de Broglie wavelength
  $$\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mE}}$$
• Electrons Accelerated Through a Potential Difference · Accelerated electron
  $$\lambda = \frac{h}{\sqrt{2meV}} \approx \frac{12.27}{\sqrt{V}}\ \text{Å}$$
• The Electron's Wave Round a Bohr Orbit · Standing wave on an orbit
  $$n\lambda = 2\pi r_n, \qquad \lambda_n = 2\pi n r_1$$

Watch out for (5)

• Writing λ ∝ 1/E
  → Wavelength, Momentum and Kinetic Energy
• Using λ = h/√(2mE) for a photon
  → Wavelength, Momentum and Kinetic Energy
• Reading 'decreased to 1/√2 times' as 'increased'
  → Electrons Accelerated Through a Potential Difference
• Picking the steepest line as the heaviest particle
  → Electrons Accelerated Through a Potential Difference
• Dividing the first-orbit circumference by n
  → The Electron's Wave Round a Bohr Orbit