To find the frequency of a photon given its energy, we can use the formula:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant, and
- [tex]\( f \)[/tex] is the frequency.
Given values:
- Energy [tex]\( E = 3.38 \times 10^{-19} \)[/tex] Joules
- Planck's constant [tex]\( h = 6.626 \times 10^{-34} \)[/tex] Joule seconds
We can rearrange the formula to solve for frequency [tex]\( f \)[/tex]:
[tex]\[ f = \frac{E}{h} \][/tex]
Substitute the given values into the formula:
[tex]\[ f = \frac{3.38 \times 10^{-19}}{6.626 \times 10^{-34}} \][/tex]
Carrying out the division, we obtain:
[tex]\[ f = 5.10 \times 10^{14} \text{ Hz} \][/tex]
Therefore, the frequency of the photon is [tex]\( 5.10 \times 10^{14} \)[/tex] Hz, which corresponds to option B.
