In the equation [tex]\( E = \frac{h c}{\lambda} \)[/tex], [tex]\( E \)[/tex] represents the energy of a photon, [tex]\( h \)[/tex] is a constant, [tex]\( c \)[/tex] is the speed of light, and [tex]\( \lambda \)[/tex] is the wavelength of the photon.
Step-by-Step Explanation:
1. Understand the Variables and Constants in the Equation:
- [tex]\( E \)[/tex]: This stands for the energy of a photon.
- [tex]\( c \)[/tex]: This is the speed of light in a vacuum, which is approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second.
- [tex]\( \lambda \)[/tex]: This represents the wavelength of the photon.
- [tex]\( h \)[/tex]: This is the unknown we are trying to identify.
2. Known Constants in Physics:
- The speed of light [tex]\( c \)[/tex] is a well-known constant in physics.
- Planck's constant [tex]\( h \)[/tex] is another fundamental constant in quantum mechanics.
- Energy [tex]\( E \)[/tex] and wavelength [tex]\( \lambda \)[/tex] are variables that can change depending on the photon.
3. Role of Each Component:
- In the equation [tex]\( E = \frac{h c}{\lambda} \)[/tex], the relationship defines how the energy of a photon is proportional to the speed of light and inversely proportional to the wavelength.
- The constant [tex]\( h \)[/tex] is necessary to bridge these proportional relationships.
4. Identify [tex]\( h \)[/tex]:
- Planck's constant is a fundamental constant in quantum mechanics that relates the energy carried by a photon to its electromagnetic wave frequency.
- Given that [tex]\( h \)[/tex] in the equation [tex]\( E = \frac{h c}{\lambda} \)[/tex] serves to relate energy and wavelength appropriately, it must be Planck's constant.
Therefore, [tex]\( h \)[/tex] in the given equation is correctly identified as Planck's constant.
Correct Answer: A. Planck's constant
