To determine the correct formula for calculating the energy of a photon, let's consider the fundamental principles of quantum physics.
The energy [tex]\( E \)[/tex] of a photon is directly related to its frequency [tex]\( f \)[/tex] via Planck's constant [tex]\( h \)[/tex]. The relationship is given by Planck's equation:
[tex]\[ E = hf \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon.
- [tex]\( h \)[/tex] is Planck's constant.
- [tex]\( f \)[/tex] is the frequency of the photon.
Let's analyze the given options one by one:
1. [tex]\( E = h - f \)[/tex]
- This option suggests a subtractive relationship between Planck's constant and the frequency, which is not correct in terms of how energy is calculated for a photon.
2. [tex]\( E = \frac{h}{f} \)[/tex]
- This option implies that the energy is given by the division of Planck's constant by the frequency. This is incorrect as it does not follow the direct proportional relationship described by Planck's equation.
3. [tex]\( E = h + f \)[/tex]
- This option suggests an additive relationship, which is not accurate as energy calculation involves multiplication of these quantities, not addition.
4. [tex]\( E = h f \)[/tex]
- This option correctly represents the relationship where the energy of a photon is the product of Planck's constant and the photon's frequency. This is the correct formula.
Thus, the correct formula for calculating the energy of a photon is:
[tex]\[ E = hf \][/tex]
Therefore, the correct choice is:
[tex]\[ E = h f \][/tex]
So the answer is the fourth option.
