Question
What do all waves carry
light
matter
particles
energy
light
matter
particles
energy
Answers
GPT-4o mini
All waves carry energy. While light waves (electromagnetic waves) do not carry matter or particles in the traditional sense, they do carry energy. Other types of waves, such as sound waves or water waves, also carry energy as they propagate through a medium.
How to determine energy in a wavelength
GPT-4o mini
The energy of a photon is related to its wavelength by the equation derived from Planck's relation, which combines concepts from quantum mechanics and wave theory. The formula is:
\[
E = \frac{hc}{\lambda}
\]
where:
- \( E \) is the energy of the photon (in joules),
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J·s}\)),
- \( c \) is the speed of light in a vacuum (\(3.00 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength of the light (in meters).
### Steps to Calculate Energy from Wavelength:
1. **Obtain the wavelength** (\( \lambda \)) of the wave in meters. If it is given in nanometers (nm), convert it to meters by using the conversion \(1 \, \text{nm} = 1 \times 10^{-9} \, \text{m}\).
2. **Plug the values into the equation**:
\[
E = \frac{(6.626 \times 10^{-34} \, \text{J·s})(3.00 \times 10^8 \, \text{m/s})}{\lambda}
\]
3. **Calculate the energy** using the above formula.
### Example:
If you have a wavelength of 500 nm (which is \(500 \times 10^{-9}\) meters):
\[
E = \frac{(6.626 \times 10^{-34} \, \text{J·s})(3.00 \times 10^{8} \, \text{m/s})}{500 \times 10^{-9} \, \text{m}}
\]
Calculating that gives:
\[
E \approx 3.98 \times 10^{-19} \, \text{J}
\]
This method allows you to determine the energy associated with any photon given its wavelength.
\[
E = \frac{hc}{\lambda}
\]
where:
- \( E \) is the energy of the photon (in joules),
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J·s}\)),
- \( c \) is the speed of light in a vacuum (\(3.00 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength of the light (in meters).
### Steps to Calculate Energy from Wavelength:
1. **Obtain the wavelength** (\( \lambda \)) of the wave in meters. If it is given in nanometers (nm), convert it to meters by using the conversion \(1 \, \text{nm} = 1 \times 10^{-9} \, \text{m}\).
2. **Plug the values into the equation**:
\[
E = \frac{(6.626 \times 10^{-34} \, \text{J·s})(3.00 \times 10^8 \, \text{m/s})}{\lambda}
\]
3. **Calculate the energy** using the above formula.
### Example:
If you have a wavelength of 500 nm (which is \(500 \times 10^{-9}\) meters):
\[
E = \frac{(6.626 \times 10^{-34} \, \text{J·s})(3.00 \times 10^{8} \, \text{m/s})}{500 \times 10^{-9} \, \text{m}}
\]
Calculating that gives:
\[
E \approx 3.98 \times 10^{-19} \, \text{J}
\]
This method allows you to determine the energy associated with any photon given its wavelength.