Question
One form of X-band radar has a frequency of 8.0 GHz , which is the same as \( 8.0 \times 10^{9} \mathrm{~Hz} \). What is the energy of the radar? \( \mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \) \( [?] \times 10^{[?]} \mathrm{J} \)
Ask by Schofield Chadwick. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The energy of the radar is \( 5.3 \times 10^{-24} \, \mathrm{J} \).
Solution
To calculate the energy \( E \) of a single photon of the radar wave, we can use the formula:
\[
E = h \nu
\]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \mathrm{J \cdot s} \))
- \( \nu \) (nu) is the frequency of the radar (\( 8.0 \times 10^{9} \, \mathrm{Hz} \))
Plugging in the values:
\[
E = 6.626 \times 10^{-34} \, \mathrm{J \cdot s} \times 8.0 \times 10^{9} \, \mathrm{Hz}
\]
\[
E = 5.3008 \times 10^{-24} \, \mathrm{J}
\]
Rounding to two significant figures:
\[
E \approx 5.3 \times 10^{-24} \, \mathrm{J}
\]
**Answer:** \( 5.3 \times 10^{-24} \mathrm{~J} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the energy of the radar, we can use the formula for energy related to frequency: \[ E = h \cdot f \] where \(E\) is the energy in joules, \(h\) is Planck's constant (\(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s}\)), and \(f\) is the frequency in hertz (\(8.0 \times 10^{9} \mathrm{~Hz}\)). Plugging in the values: \[ E = 6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \cdot 8.0 \times 10^{9} \mathrm{~Hz} \] Calculating this gives: \[ E = 5.3008 \times 10^{-24} \mathrm{~J} \] So, the energy of the radar is approximately \(5.3 \times 10^{-24} \mathrm{~J}\). The answer is: \(5.3 \times 10^{-24} \mathrm{~J}\)
