To find the frequency of a photon given its energy, we can use the well-known relationship in quantum mechanics expressed by Planck's equation:
[tex]\[ E = h \cdot f \][/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.
Given:
- [tex]\( E = 3.4 \times 10^{-18} \)[/tex] joules,
- [tex]\( h = 6.63 \times 10^{-34} \)[/tex] joules·second,
we need to find the frequency [tex]\( f \)[/tex]. Rearrange the equation to solve for [tex]\( f \)[/tex]:
[tex]\[ f = \frac{E}{h} \][/tex]
Substitute the given values into the equation:
[tex]\[ f = \frac{3.4 \times 10^{-18}}{6.63 \times 10^{-34}} \][/tex]
When you carry out this division, you get:
[tex]\[ f = 5.128205128205129 \times 10^{15} \][/tex]
This value can be approximated to scientific notation as:
[tex]\[ f \approx 5.12 \times 10^{15} \text{ Hz} \][/tex]
Thus, the frequency of the photon is [tex]\( 5.12 \times 10^{15} \)[/tex] Hz. Therefore, the correct answer is:
[tex]\[ \boxed{5.12 \times 10^{15} \text{ Hz}} \][/tex]
