Here is a quantum question: Calculate the energy of a photon of green light with a wavelength of $550 \text{ nm}$. • Planck's constant ($h$) = $6.626 \times 10^{-34} \text{ J}\cdot\text{s}$ • Speed of light ($c$) = $3.00 \times 10^8 \text{ m/s}$ Step 1: Identify the given values and constants. • Wavelength ($\lambda$) = $550 \text{ nm}$ • Planck's constant ($h$) = $6.626 \times 10^{-34} \text{ J}\cdot\text{s}$ • Speed of light ($c$) = $3.00 \times 10^8 \text{ m/s}$ Step 2: Convert the wavelength from nanometers to meters. $$1 \text{ nm} = 10^{-9} \text{ m}$$ $$\lambda = 550 \text{ nm} \times \frac{10^{-9} \text{ m}}{1 \text{ nm}}$$ $$\lambda = 5.50 \times 10^{-7} \text{ m}$$ Step 3: Calculate the frequency ($f$) of the photon using the relationship between speed of light, wavelength, and frequency. The formula is $c = \lambda f$. Rearrange to solve for $f$: $$f = \frac{c}{\lambda}$$ Substitute the values: $$f = \frac{3.00 \times 10^8 \text{ m/s}}{5.50 \times 10^{-7} \text{ m}}$$ $$f \approx 5.4545 \times 10^{14} \text{ Hz}$$ Step 4: Calculate the energy ($E$) of the photon using Planck's equation. The formula is $E = hf$. Substitute the values: $$E = (6.626 \times 10^{-34} \text{ J}\cdot\text{s}) \times (5.4545 \times 10^{14} \text{ Hz})$$ $$E \approx 3.61 \times 10^{-19} \text{ J}$$ The energy of the photon is $\boxed{3.61 \times 10^{-19} \text{ J}}$.