To determine the frequency of a wave given its energy and Planck's constant, we use the relationship defined by Planck's equation, which is:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the wave,
- [tex]\( h \)[/tex] is Planck's constant,
- [tex]\( f \)[/tex] is the frequency of the wave.
We are given the energy [tex]\( E \)[/tex] of the wave as [tex]\( 2.64 \times 10^{-21} \)[/tex] joules and Planck's constant [tex]\( h \)[/tex] as [tex]\( 6.6 \times 10^{-34} \)[/tex] joule-seconds. We need to find the frequency [tex]\( f \)[/tex], which can be determined by rearranging Planck's equation to solve for [tex]\( f \)[/tex]:
[tex]\[ f = \frac{E}{h} \][/tex]
Substituting the given values:
[tex]\[ f = \frac{2.64 \times 10^{-21}}{6.6 \times 10^{-34}} \][/tex]
Performing the division:
[tex]\[ f = 4.00 \times 10^{12} \ \text{hertz} \][/tex]
Thus, the frequency of the wave is [tex]\( 4.00 \times 10^{12} \)[/tex] hertz. This matches option:
A. [tex]\( 4.00 \times 10^{12} \)[/tex] hertz.
