To find the energy of an electromagnetic wave given its frequency, we can use Planck's equation:
[tex]\[ E = hf \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [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 electromagnetic wave.
Given the frequency [tex]\( f = 8 \times 10^{12} \text{ Hz} \)[/tex], we can substitute the values into the equation:
[tex]\[ E = (6.626 \times 10^{-34} \text{ J} \cdot \text{s}) \times (8 \times 10^{12} \text{ Hz}) \][/tex]
Multiplying these values together:
[tex]\[ E = 5.3008 \times 10^{-21} \text{ J} \][/tex]
Thus, the energy of the electromagnetic wave is:
[tex]\[ E = 5.3008 \times 10^{-21} \text{ J} \][/tex]
The closest option to this value is:
C. [tex]\( 5.3 \times 10^{-21} \text{ J} \)[/tex]
Therefore, the correct answer is:
C. [tex]\( 5.3 \times 10^{-21} \text{ J} \)[/tex]
