Select the correct answer.

The energy of a given wave in the electromagnetic spectrum is [tex][tex]$2.64 \times 10^{-21}$[/tex][/tex] joules, and the value of Planck's constant is [tex][tex]$6.6 \times 10^{-34}$[/tex][/tex] joule-seconds. What is the value of the frequency of the wave?

A. [tex][tex]$4.00 \times 10^{12}$[/tex][/tex] hertz
B. [tex][tex]$2.34 \times 10^{-12}$[/tex][/tex] hertz
C. [tex][tex]$1.30 \times 10^{13}$[/tex][/tex] hertz
D. [tex][tex]$2.52 \times 10^{-6}$[/tex][/tex] hertz
E. [tex][tex]$8.11 \times 10^{-7}$[/tex][/tex] hertz



Answer :

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.