Question

Calculate the energy of a red light photon whose frequency is 700nm

Answer 1

To calculate the energy of a photon, you can use the equation:

\[
E = h \cdot f
\]

where:
- \(E\) is the energy of the photon in joules,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}\)),
- \(f\) is the frequency of the light in hertz (Hz).

First, we need to convert the wavelength of red light, which is given as 700 nm, to frequency using the speed of light equation:

\[
c = \lambda \cdot f
\]

where:
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters,
- \(f\) is the frequency in hertz.

**Step 1: Convert 700 nm to meters:**

\[
700 \, \text{nm} = 700 \times 10^{-9} \, \text{m} = 7.00 \times 10^{-7} \, \text{m}
\]

**Step 2: Calculate the frequency:**

\[
f = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \, \text{m/s}}{7.00 \times 10^{-7} \, \text{m}}
\]

Calculating that:

\[
f \approx 4.29 \times 10^{14} \, \text{Hz}
\]

**Step 3: Calculate the energy:**

Now, we can substitute the frequency back into the energy equation:

\[
E = h \cdot f = (6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \cdot (4.29 \times 10^{14} \, \text{Hz})
\]

Calculating that:

\[
E \approx 2.84 \times 10^{-19} \, \text{J}
\]

So, the energy of a red light photon with a frequency corresponding to 700 nm is approximately \(2.84 \times 10^{-19} \, \text{J}\).