To find the energy of a photon, you can use the formula:
[tex]\[ E = h \nu \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\(6.63 \times 10^{-34} \)[/tex] J·s),
- [tex]\( \nu \)[/tex] (or [tex]\( f \)[/tex]) is the frequency of the photon.
Given the frequency of the photon ([tex]\(\nu\)[/tex]) is [tex]\(2.2 \times 10^{16} \)[/tex] Hz and Planck's constant ([tex]\( h \)[/tex]) is [tex]\(6.63 \times 10^{-34} \)[/tex] J·s, substitute these values into the formula to calculate the energy of the photon:
[tex]\[ E = (6.63 \times 10^{-34} \text{ J·s}) \times (2.2 \times 10^{16} \text{ Hz}) \][/tex]
When you perform this multiplication, the energy [tex]\( E \)[/tex] of the photon is:
[tex]\[ E = 1.4586 \times 10^{-17} \text{ J} \][/tex]
So, the energy of the photon with a frequency of [tex]\(2.2 \times 10^{16} \)[/tex] Hz is approximately [tex]\(1.5 \times 10^{-17} \)[/tex] J.
Therefore, the correct answer is:
[tex]\[ \boxed{1.5 \times 10^{-17} \text{ J}} \][/tex]
