To determine the frequency of an electromagnetic wave given its energy, we can use the relationship between energy (E) and frequency (f) defined by Planck's equation:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the wave.
- [tex]\( h \)[/tex] is Planck's constant, which is approximately [tex]\( 6.62607015 \times 10^{-34} \)[/tex] J·s.
- [tex]\( f \)[/tex] is the frequency of the wave.
We need to find the frequency [tex]\( f \)[/tex]. Rearranging the formula to solve for [tex]\( f \)[/tex] gives us:
[tex]\[ f = \frac{E}{h} \][/tex]
Given:
[tex]\[ E = 5.0 \times 10^{-20} \, \text{J} \][/tex]
[tex]\[ h = 6.62607015 \times 10^{-34} \, \text{J·s} \][/tex]
Substitute the given values into the rearranged formula:
[tex]\[ f = \frac{5.0 \times 10^{-20}}{6.62607015 \times 10^{-34}} \][/tex]
This calculation results in:
[tex]\[ f \approx 75459508982107.6 \, \text{Hz} \][/tex]
Now, we compare this result with the given options:
A. [tex]\( 3.98 \times 10^{-6} \, \text{Hz} \)[/tex]
B. [tex]\( 5.22 \times 10^5 \, \text{Hz} \)[/tex]
C. [tex]\( 1.67 \times 10^{-28} \, \text{Hz} \)[/tex]
D. [tex]\( 7.55 \times 10^{13} \, \text{Hz} \)[/tex]
The calculated frequency [tex]\( 75459508982107.6 \, \text{Hz} \)[/tex] is equivalent to [tex]\( 7.55 \times 10^{13} \, \text{Hz} \)[/tex], which corresponds to option D.
Therefore, the correct answer is:
[tex]\[ \boxed{7.55 \times 10^{13} \, \text{Hz}} \][/tex]
- Option D
