To determine the energy of the electromagnetic radiation from the microwave, we can use the relationship given by Planck's equation:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the electromagnetic radiation,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\( 6.626 \times 10^{-34} \)[/tex] J·s),
- [tex]\( f \)[/tex] is the frequency of the electromagnetic radiation.
Given:
- The frequency [tex]\( f \)[/tex] is [tex]\( 90 \)[/tex] GHz, which is equivalent to [tex]\( 9.0 \times 10^{10} \)[/tex] Hz,
- Planck's constant [tex]\( h \)[/tex] is [tex]\( 6.626 \times 10^{-34} \)[/tex] J·s.
Substitute the given values into Planck's equation:
[tex]\[ E = (6.626 \times 10^{-34} \, \text{J·s}) \times (9.0 \times 10^{10} \, \text{Hz}) \][/tex]
Multiplying these values together, we get:
[tex]\[ E = 5.9634 \times 10^{-23} \, \text{J} \][/tex]
Thus, the energy of the electromagnetic radiation from the microwave is:
[tex]\[ 5.9634 \times 10^{-23} \, \text{J} \][/tex]
