To determine the energy of a photon emitted by a helium-neon laser with a wavelength of 632.8 nm, we need to follow several steps.
### Step 1: Convert the wavelength from nanometers to meters
The wavelength given is [tex]\( \lambda = 632.8 \)[/tex] nm. Since 1 nanometer (nm) is [tex]\( 10^{-9} \)[/tex] meters, we convert the wavelength to meters:
[tex]\[
\lambda = 632.8 \times 10^{-9} \ \text{m} = 6.328 \times 10^{-7} \ \text{m}
\][/tex]
### Step 2: Calculate the frequency of the light
The speed of light ([tex]\( c \)[/tex]) in a vacuum is approximately [tex]\( 3 \times 10^{8} \ \text{m/s} \)[/tex]. The relationship between the speed of light, wavelength, and frequency ([tex]\( f \)[/tex]) is given by:
[tex]\[
c = \lambda f
\][/tex]
Rearranging this equation to solve for the frequency ([tex]\( f \)[/tex]):
[tex]\[
f = \frac{c}{\lambda}
\][/tex]
Substitute the known values into the equation:
[tex]\[
f = \frac{3 \times 10^{8} \ \text{m/s}}{6.328 \times 10^{-7} \ \text{m}} \approx 4.740834386852086 \times 10^{14} \ \text{Hz}
\][/tex]
### Step 3: Calculate the energy of one photon
The energy ([tex]\( E \)[/tex]) of a photon can be calculated using Planck's equation, which relates the energy of a photon to its frequency:
[tex]\[
E = hf
\][/tex]
where [tex]\( h \)[/tex] is Planck's constant ([tex]\( 6.626 \times 10^{-34} \ \text{J} \cdot \text{s} \)[/tex]).
Substitute the known values into the equation:
[tex]\[
E = (6.626 \times 10^{-34} \ \text{J} \cdot \text{s}) \times (4.740834386852086 \times 10^{14} \ \text{Hz}) \approx 3.141276864728192 \times 10^{-19} \ \text{J}
\][/tex]
### Summary of Results
- Wavelength: [tex]\( 6.328 \times 10^{-7} \ \text{m} \)[/tex]
- Frequency: [tex]\( 4.740834386852086 \times 10^{14} \ \text{Hz} \)[/tex]
- Energy of one photon: [tex]\( 3.141276864728192 \times 10^{-19} \ \text{J} \)[/tex]
Thus, the energy of a photon of light emitted by the helium-neon laser with a wavelength of 632.8 nm is approximately [tex]\( 3.141276864728192 \times 10^{-19} \ \text{J} \)[/tex].
