Question
What is the energy of a photon with a frequency of 1.7 × 1017 Hz? Planck’s constant is 6.63 × 10–34 J•s.
1.1 × 10–17 J
1.1 × 10–16 J
8.3 × 10–16 J
8.3 × 10–15 J
1.1 × 10–17 J
1.1 × 10–16 J
8.3 × 10–16 J
8.3 × 10–15 J
Answers
GPT-4o mini
To find the energy of a photon given its frequency, you can use the formula:
\[
E = h \cdot f
\]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{J s}\)),
- \(f\) is the frequency of the photon (\(1.7 \times 10^{17} \, \text{Hz}\)).
Now we can calculate the energy:
\[
E = (6.63 \times 10^{-34} \, \text{J s}) \times (1.7 \times 10^{17} \, \text{Hz})
\]
Calculating this:
\[
E = 6.63 \times 1.7 \times 10^{-34 + 17} \, \text{J}
\]
\[
E = 11.271 \times 10^{-17} \, \text{J}
\]
Now adjusting the exponent:
\[
E = 1.1271 \times 10^{-16} \, \text{J}
\]
This can be rounded to:
\[
E \approx 1.1 \times 10^{-16} \, \text{J}
\]
Thus, the energy of the photon is **1.1 × 10–16 J**.
\[
E = h \cdot f
\]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{J s}\)),
- \(f\) is the frequency of the photon (\(1.7 \times 10^{17} \, \text{Hz}\)).
Now we can calculate the energy:
\[
E = (6.63 \times 10^{-34} \, \text{J s}) \times (1.7 \times 10^{17} \, \text{Hz})
\]
Calculating this:
\[
E = 6.63 \times 1.7 \times 10^{-34 + 17} \, \text{J}
\]
\[
E = 11.271 \times 10^{-17} \, \text{J}
\]
Now adjusting the exponent:
\[
E = 1.1271 \times 10^{-16} \, \text{J}
\]
This can be rounded to:
\[
E \approx 1.1 \times 10^{-16} \, \text{J}
\]
Thus, the energy of the photon is **1.1 × 10–16 J**.