To determine the frequency of the wave, we will use the relationship between energy ([tex]\(E\)[/tex]), Planck's constant ([tex]\(h\)[/tex]), and frequency ([tex]\(f\)[/tex]). The formula for this relationship is:
[tex]\[ E = h \cdot f \][/tex]
We need to find the frequency, so we rearrange the formula to solve for [tex]\(f\)[/tex]:
[tex]\[ f = \frac{E}{h} \][/tex]
Given:
- The energy [tex]\(E\)[/tex] of the wave is [tex]\(2.64 \times 10^{-21}\)[/tex] joules.
- Planck's constant [tex]\(h\)[/tex] is [tex]\(6.6 \times 10^{-34}\)[/tex] joule seconds.
Substituting the given values into the equation:
[tex]\[ f = \frac{2.64 \times 10^{-21}}{6.6 \times 10^{-34}} \][/tex]
Now, perform the division:
[tex]\[ f = \frac{2.64}{6.6} \times \frac{10^{-21}}{10^{-34}} \][/tex]
Simplifying the coefficients:
[tex]\[ \frac{2.64}{6.6} = 0.4 \][/tex]
Simplifying the exponents:
[tex]\[ \frac{10^{-21}}{10^{-34}} = 10^{13} \][/tex]
Combining these, we get:
[tex]\[ f = 0.4 \times 10^{13} \][/tex]
Or equivalently:
[tex]\[ f = 4.00 \times 10^{12} \][/tex]
Therefore, the frequency [tex]\(f\)[/tex] of the wave is:
[tex]\[ 4.00 \times 10^{12} \text{ hertz} \][/tex]
The correct answer is:
A. [tex]\(4.00 \times 10^{12}\)[/tex] hertz
