To determine the frequency of the photon given the energy and Planck's constant, we can use the formula that relates energy ([tex]\(E\)[/tex]) to frequency ([tex]\(f\)[/tex]):
[tex]\[ E = h \cdot f \][/tex]
Here, [tex]\(E\)[/tex] is the energy of the photon, [tex]\(h\)[/tex] is Planck's constant, and [tex]\(f\)[/tex] is the frequency we want to find.
Given:
- Energy ([tex]\(E\)[/tex]) = [tex]\(3.4 \times 10^{-18}\)[/tex] joules
- Planck's constant ([tex]\(h\)[/tex]) = [tex]\(6.63 \times 10^{-34}\)[/tex] joules·seconds
We need to solve for [tex]\(f\)[/tex]:
[tex]\[ f = \frac{E}{h} \][/tex]
Substituting the given values into the equation:
[tex]\[ f = \frac{3.4 \times 10^{-18} \, \text{J}}{6.63 \times 10^{-34} \, \text{J} \cdot \text{s}} \][/tex]
Carrying out the division, we get:
[tex]\[ f = 5.12 \times 10^{15} \, \text{Hz} \][/tex]
Therefore, the frequency of the photon is:
[tex]\[ 5.12 \times 10^{15} \, \text{Hz} \][/tex]
Thus, the correct answer is:
[tex]\[ 5.12 \times 10^{15} \, \text{Hz} \][/tex]
