11Class 12 Physics

Dual Nature of Radiation and Matter formulas

Photoelectric effect and de Broglie formulas for Dual Nature of Radiation and Matter. It's short and scoring, with mostly direct numericals.

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All Physics formulas

Photoelectric effect

Photon energy: $\displaystyle E = h\nu = \frac{hc}{\lambda}$
hc ≈ 1240 eV nm.
Photon momentum: $\displaystyle p = \frac{h\nu}{c} = \frac{h}{\lambda}$
Einstein's equation: $\displaystyle K_{\max} = h\nu - \phi_0$
Stopping potential: $\displaystyle eV_0 = K_{\max}$
Work function: $\displaystyle \phi_0 = h\nu_0$
ν₀ is the threshold frequency.

Matter waves

de Broglie wavelength: $\displaystyle \lambda = \frac{h}{p} = \frac{h}{mv}$
From kinetic energy: $\displaystyle \lambda = \frac{h}{\sqrt{2mK}}$
Electron through potential V: $\displaystyle \lambda = \frac{1.227}{\sqrt V}\ \text{nm}$

Where students slip up

Thinking brighter light gives faster electrons. Intensity changes the number of electrons, and frequency changes their energy.
Expecting emission below the threshold frequency, however bright the light. It doesn't happen.
Mixing units. Convert between eV and joules before using E = hν in SI.

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