The question asks for the formula to calculate the energy of a photon. To solve this, let's start by understanding the essential parameters involved:
1. Photons are elementary particles of light that carry energy.
2. Planck's constant (h) is a fundamental constant in quantum mechanics, approximately equal to [tex]\(6.62607015 \times 10^{-34}\)[/tex] m[tex]\(^{2}\)[/tex] kg / s.
3. Frequency (f): This is the number of cycles per second of the wave, measured in Hertz (Hz).
The energy of a photon is directly proportional to its frequency - this means that as the frequency of the photon increases, so does its energy.
According to quantum theory, the relationship between the energy of a photon (E), Planck's constant (h), and the frequency of the photon (f) is given by the formula:
[tex]\[ E = h \cdot f \][/tex]
Given the options provided:
1. [tex]\( E = h - f \)[/tex]
2. [tex]\( E = \frac{h}{f} \)[/tex]
3. [tex]\( E = h + f \)[/tex]
4. [tex]\( E = h \cdot f \)[/tex]
We can identify that the fourth option, [tex]\( E = h \cdot f \)[/tex], is the correct formula for calculating the energy of a photon.
Thus, the correct answer is:
[tex]\[ E = h \cdot f \][/tex]
So, the correct option is:
[tex]\[ \boxed{4} \][/tex]
