Compute the energy per cm squared for a ideal blackbody at 300K 

	 

Compute the energy a photon at 0.55 microns carries 

	 

Compute the number of photons from an LED emitting 10W of light at 0.65 microns (see the in class example from Week 2) 

	 

Compute the average emissivity of an opaque object with an average albedo of 0.5 in the visible spectrum 

	 

Compute the peak wavelength for a blackbody at 2000K, 5000K, and 10000 

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

Compute the energy per cm squared for an ideal blackbody at 300K, compute the energy a photon at 0.55 microns carries, compute the number of photons from an LED emitting 10W of light at 0.65 microns, compute the average emissivity of an opaque object with an average albedo of 0.5 in the visible spectrum, and compute the peak wavelength for a blackbody at 2000K, 5000K, and 10000K.

Learn how to compute energy per cm² for an ideal blackbody at 300K, the energy of a photon at 0.55 microns, the number of photons emitted by an LED at 0.65 microns, and the peak wavelength of blackbodies at 2000K, 5000K, and 10000K. This guide covers key physics concepts including Stefan-Boltzmann law, photon energy, and Wien's displacement law.

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