Let's solve the problem step-by-step:
1. Identify the given quantities:
- The frequency of the photon ([tex]\( \nu \)[/tex]) is [tex]\( 1.7 \times 10^{17} \, \text{Hz} \)[/tex].
- Planck's constant ([tex]\( h \)[/tex]) is [tex]\( 6.63 \times 10^{-34} \, \text{J} \cdot \text{s} \)[/tex].
2. Recall the formula to calculate the energy of a photon:
[tex]\[
E = h \nu
\][/tex]
where
[tex]\( E \)[/tex] is the energy,
[tex]\( h \)[/tex] is Planck's constant, and
[tex]\( \nu \)[/tex] is the frequency.
3. Substitute the given values into the formula:
[tex]\[
E = (6.63 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (1.7 \times 10^{17} \, \text{Hz})
\][/tex]
4. Perform the multiplication:
[tex]\[
E = 6.63 \times 1.7 \times 10^{-34 + 17} \, \text{J}
\][/tex]
5. Simplify the numerical part:
[tex]\[
6.63 \times 1.7 = 11.271
\][/tex]
And combine the exponents:
[tex]\[
10^{-34 + 17} = 10^{-17}
\][/tex]
6. Combine the numerical and exponential parts:
[tex]\[
E = 11.271 \times 10^{-17} \, \text{J}
\][/tex]
7. Convert to scientific notation:
[tex]\[
E \approx 1.1271 \times 10^{-16} \, \text{J}
\][/tex]
8. Round appropriately and match to the given options:
The closest option is:
[tex]\[
1.1 \times 10^{-16} \, \text{J}
\][/tex]
Therefore, the energy of the photon is [tex]\( 1.1 \times 10^{-16} \, \text{J} \)[/tex].
