Calculating the Energy of Light:
Planck's constant is a fundamental constant in physics that describes the size of the energy packets (quanta) contained in light. The energy in light is not continuous but in the form of packets of energy with a specific size. Each of these packets of energy is called a 'quantum'. The quantum of light energy is called a photon.
Assuming that Planck's constant, 𝒉 = (\(6.626 \times 10^{-34}\text{ J}\cdot\text{s}\)) and that f is the frequency of the light wave in Hertz; Hz or s-1; then the frequency of any wave is related to its wavelength via c=fλ.
Given that the speed of light (\(c \approx 3.0 \times 10^8\text{ m/s}\)); then \(f = \frac{c}{\lambda}\), and \(E = \frac{h \cdot c}{\lambda} = h \cdot f\).
A] Calculation for Red Light (Low Energy End):
Wavelength (λ): \(\sim 700\text{ nm}\) (\(7.0 \times 10^{-7}\text{ m}\))
Frequency (f): \(\frac{3.0 \times 10^8\text{ m/s}}{7.0 \times 10^{-7}\text{ m}} \approx 4.28 \times 10^{14}\text{ Hz}\)
Energy (E=hf): \((6.626 \times 10^{-34}\text{ J}\cdot\text{s}) \cdot (4.28 \times 10^{14}\text{ s}^{-1}) \approx \mathbf{2.84 \times 10^{-19}\text{ J}}\) (\(1.77\text{ eV}\))
B] Calculation for Violet Light (High Energy End):
Wavelength (λ): \(\sim 400\text{ nm}\) (\(4.0 \times 10^{-7}\text{ m}\))
Frequency (f): \(\frac{3.0 \times 10^8\text{ m/s}}{4.0 \times 10^{-7}\text{ m}} \approx 7.49 \times 10^{14}\text{ Hz}\)
Energy (E=hf): \((6.626 \times 10^{-34}\text{ J}\cdot\text{s}) \cdot (7.49 \times 10^{14}\text{ s}^{-1}) \approx \mathbf{4.97 \times 10^{-19}\text{ J}}\) (\(3.10\text{ eV}\))
