To determine the frequency of electromagnetic radiation that will have an energy of [tex]\( 3.35 \times 10^{-18} \)[/tex] Joules given Planck's constant ([tex]\( h \)[/tex]) is [tex]\( 6.63 \times 10^{-4} \)[/tex] Joule-seconds, we can use the relationship provided by Planck's equation, which is:
[tex]\[ E = h \times f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy,
- [tex]\( h \)[/tex] is Planck's constant,
- [tex]\( f \)[/tex] is the frequency.
Here, we need to solve for the frequency ([tex]\( f \)[/tex]). Rearranging the equation to solve for [tex]\( f \)[/tex], we get:
[tex]\[ f = \frac{E}{h} \][/tex]
Now, plug in the given values:
[tex]\[ E = 3.35 \times 10^{-18} \, \text{J} \][/tex]
[tex]\[ h = 6.63 \times 10^{-4} \, \text{J} \cdot \text{s} \][/tex]
Thus,
[tex]\[ f = \frac{3.35 \times 10^{-18}}{6.63 \times 10^{-4}} \][/tex]
Performing the division:
[tex]\[ f \approx 5.052790346907994 \times 10^{-15} \, \text{Hz} \][/tex]
Now, looking at the given options, none of the choices directly match the exact value calculated. However, if we reconsider the magnitude, the closest option to our calculated frequency seems incorrectly represented in scientific notation in the context of this problem.
Given that [tex]\( 5.052790346907994 \times 10^{-15} \, \text{Hz} \)[/tex] is significantly away from the options provided, it seems there is no exact match for this problem format.
Nonetheless, by properly understanding the scientific notation and typical numerical value expressions for frequencies in the context provided, the method and steps to find the correct value are correctly followed. In the context provided, 5.06 x 10^5 Hz would not be a suitable numerical answer; yet the method remains intact as required.
