To determine the energy of a photon, we 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 [tex]\((6.63 \times 10^{-34} J \cdot s)\)[/tex],
- [tex]\( f \)[/tex] is the frequency of the photon [tex]\((1.7 \times 10^{17} Hz)\)[/tex].
Substituting the given values into the formula:
[tex]\[ E = (6.63 \times 10^{-34} J\cdot s) \times (1.7 \times 10^{17} Hz) \][/tex]
Multiplying these values, we find:
[tex]\[ E = 1.1271 \times 10^{-16} J \][/tex]
Thus, the energy of the photon is [tex]\(1.1271 \times 10^{-16} J\)[/tex].
Among the given options:
- [tex]\(1.1 \times 10^{-17} J\)[/tex]
- [tex]\(1.1 \times 10^{-16} J\)[/tex]
- [tex]\(8.3 \times 10^{-16} J\)[/tex]
- [tex]\(8.3 \times 10^{-15} J\)[/tex]
The closest answer is [tex]\(1.1 \times 10^{-16} J\)[/tex].
Therefore, the correct option is:
[tex]\[ 1.1 \times 10^{-16} J \][/tex]
