Question
What is the frequency of yellow light with an energy of \( 3.4 \times 10^{-19} \mathrm{~J} \) ? \[ \begin{array}{c}\mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \\ {[?] \times 10^{[?]} \mathrm{Hz}}\end{array} \]
Ask by Cruz Ayala. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The frequency of the yellow light is \( 5.13 \times 10^{14} \) Hz.
Solution
To determine the frequency (\( f \)) of yellow light with an energy (\( E \)) of \( 3.4 \times 10^{-19} \) joules, you can use the relationship between energy and frequency given by Planck's equation:
\[
E = h \cdot f
\]
Where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \mathrm{J \cdot s} \)),
- \( f \) is the frequency of the light.
Rearranging the equation to solve for \( f \):
\[
f = \frac{E}{h}
\]
Plugging in the known values:
\[
f = \frac{3.4 \times 10^{-19} \, \mathrm{J}}{6.626 \times 10^{-34} \, \mathrm{J \cdot s}} = \frac{3.4}{6.626} \times 10^{(-19) - (-34)} \, \mathrm{Hz}
\]
\[
f \approx 0.513 \times 10^{15} \, \mathrm{Hz}
\]
This can be expressed in standard scientific notation as:
\[
f \approx 5.13 \times 10^{14} \, \mathrm{Hz}
\]
**Final Answer:**
The frequency of the yellow light is \( 5.13 \times 10^{14} \) Hz.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the frequency of yellow light given its energy, we can use the equation: \[ E = h \cdot f, \] where \( E \) is energy, \( h \) is Planck's constant, and \( f \) is frequency. Rearranging the formula to solve for frequency gives: \[ f = \frac{E}{h}. \] Substituting the provided values: \[ f = \frac{3.4 \times 10^{-19} \mathrm{~J}}{6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}}. \] Calculating that, we get: \[ f \approx 5.13 \times 10^{14} \mathrm{~Hz}. \] So, the frequency of yellow light is approximately \( 5.13 \times 10^{14} \mathrm{~Hz} \).
