Let's compute each of these values step by step:

1. Energy per cm² for a blackbody at 300 K

We can use the Stefan-Boltzmann law to calculate the energy per unit area emitted by a blackbody: $E = \sigma T^4$ Where:

• $\sigma$ is the Stefan-Boltzmann constant, $\sigma = 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4$
• $T = 300 \, \text{K}$

Since the question asks for energy per cm², we need to convert the result from m² to cm² (1 m² = 10,000 cm²).

$E = (5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4)(300 \, \text{K})^4 = \sigma T^4$

Let me compute this for you.

2. Energy of a photon at 0.55 microns

The energy of a photon is given by: $E = \frac{hc}{\lambda}$ Where:

• $h = 6.626 \times 10^{-34} \, \text{J·s}$ is Planck's constant
• $c = 3 \times 10^8 \, \text{m/s}$ is the speed of light
• $\lambda = 0.55 \, \mu m = 0.55 \times 10^{-6} \, \text{m}$ is the wavelength

Substitute the values into the equation to find the energy.

3. Number of photons from an LED emitting 10W of light at 0.65 microns

First, we calculate the energy of a single photon at 0.65 microns using the same formula: $E_{\text{photon}} = \frac{hc}{\lambda}$ Where $\lambda = 0.65 \, \mu m = 0.65 \times 10^{-6} \, \text{m}$.

Next, we calculate the total number of photons emitted