Solve quantum questions for me

Question

ScanSolve AI Tutor · Accepted Answer

Here is a quantum question:

Calculate the energy of a photon of green light with a wavelength of $550 \text{ nm}$ .

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 ( $c$ ) = $3.00 \times 10^8 \text{ m/s}$
Convert the wavelength from nanometers to meters.
$1 \text{ nm} = 10^{-9} \text{ m}$ $\lambda = 550 \text{ nm} \times \frac{10^{-9} \text{ m}}{1 \text{ nm}}$ $\lambda = 5.50 \times 10^{-7} \text{ m}$
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:
$f = \frac{3.00 \times 10^8 \text{ m/s}}{5.50 \times 10^{-7} \text{ m}}$ $f \approx 5.4545 \times 10^{14} \text{ Hz}$
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 $3.61 \times 10^{-19} \text{ J}$ .

Answer