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# PLANCK'S CONSTANT In quantum mechanics, energy is related to frequency by **Planck's constant**: $E = h f$ where * $E$ is energy, * $f$ is frequency, and * $h \approx 6.626 \times 10^{-34} Js \approx 4.136 \times 10^{-15} eVs$ **Example:** A photon of green light has a frequency of $600...

# PLANCK'S CONSTANT In quantum mechanics, energy is related to frequency by **Planck's constant**: $E = h f$ where * $E$ is energy, * $f$ is frequency, and * $h \approx 6.626 \times 10^{-34} Js \approx 4.136 \times 10^{-15} eVs$ **Example:** A photon of green light has a frequency of $600 \times 10^{12} Hz$. How much energy does it carry? $E = hf = (6.626 \times 10^{-34} Js)(600 \times 10^{12} Hz) = 3.98 \times 10^{-19} J$ ## WAVE - PARTICLE DUALITY Light and matter behave as both waves and particles. * Light and matter propagate through space like waves. * Light and matter exchange energy like particles. ## UNCERTAINTY PRINCIPLE It is impossible to know both the position and momentum of a particle with perfect accuracy. $\Delta x \Delta p \geq \frac{h}{4\pi}$ where * $\Delta x$ is the uncertainty in position, * $\Delta p$ is the uncertainty in momentum, and * $h$ is Planck's constant. **Example:** An electron is known to be within $1 \mu m$ of a certain point. What is the minimum uncertainty in its speed? $\Delta x \Delta p \geq \frac{h}{4\pi}$ $\Delta x m \Delta v \geq \frac{h}{4\pi}$ $\Delta v \geq \frac{h}{4\pi m \Delta x} = \frac{6.626 \times 10^{-34} Js}{4\pi (9.109 \times 10^{-31} kg)(1 \times 10^{-6} m)} = 57.9 \frac{m}{s}$