To determine the energy of an electromagnetic wave given its frequency, we can use Planck's equation, which is expressed as:
[tex]\[ E = h \times f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the wave,
- [tex]\( h \)[/tex] is Planck's constant, [tex]\( 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \)[/tex],
- [tex]\( f \)[/tex] is the frequency of the wave.
Given data:
- The frequency [tex]\( f \)[/tex] of the wave is [tex]\( 8 \times 10^{12} \text{ Hz} \)[/tex].
Now, we substitute the given values into the equation:
[tex]\[ E = (6.626 \times 10^{-34} \text{ J} \cdot \text{s}) \times (8 \times 10^{12} \text{ Hz}) \][/tex]
When we compute the product:
[tex]\[ E = 8 \times 6.626 \times 10^{-34+12} \][/tex]
[tex]\[ E = 53.008 \times 10^{-22} \][/tex]
[tex]\[ E = 5.3008 \times 10^{-21} \text{ J} \][/tex]
Thus, the energy of the electromagnetic wave is [tex]\( 5.3008 \times 10^{-21} \text{ J} \)[/tex].
Among the given options, the correct answer is:
D. [tex]\( 5.3 \times 10^{-21} \text{ J} \)[/tex]
