To solve this problem, we need to find the energy of a photon given its frequency and Planck's constant.
1. Identify the given values:
- Frequency of the photon ([tex]\(f\)[/tex]): [tex]\(2.9 \times 10^{-16} \, \text{Hz}\)[/tex]
- Planck's constant ([tex]\(h\)[/tex]): [tex]\(6.63 \times 10^{-34} \, \text{J} \cdot \text{s}\)[/tex]
2. Use the formula to calculate the energy of the photon:
[tex]\[
E = h \times f
\][/tex]
where [tex]\(E\)[/tex] is the energy, [tex]\(h\)[/tex] is Planck's constant, and [tex]\(f\)[/tex] is the frequency.
3. Substitute the given values into the formula:
[tex]\[
E = (6.63 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (2.9 \times 10^{-16} \, \text{Hz})
\][/tex]
4. Perform the multiplication:
[tex]\[
E = 1.9227 \times 10^{-49} \, \text{J}
\][/tex]
5. Express the energy in the required format (nearest tenths place in the form of [tex]\(x \times 10^{-49} \, \text{J}\)[/tex]):
The calculated energy [tex]\(E = 1.9227 \times 10^{-49} \, \text{J}\)[/tex] can be rounded to the nearest tenths place.
6. Rounding the energy to the nearest tenths place:
[tex]\[
1.9227 \approx 1.9
\][/tex]
So, the energy of the photon, to the nearest tenths place, is [tex]\(1.9 \times 10^{-49} \, \text{J}\)[/tex].
