To find the energy of light with a frequency of [tex]\(3 \times 10^9\)[/tex] Hz, we use the formula for the energy of a photon:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\(6.626 \times 10^{-34} \)[/tex] J·s),
- [tex]\( f \)[/tex] is the frequency of the light ([tex]\(3 \times 10^9 \)[/tex] Hz).
Substitute the given values into the formula:
[tex]\[ E = (6.626 \times 10^{-34} \, \text{J·s}) \times (3 \times 10^9 \, \text{Hz}) \][/tex]
Multiplying these values:
[tex]\[ E = 6.626 \times 3 \times 10^{-34 + 9} \][/tex]
[tex]\[ E = 19.878 \times 10^{-25} \][/tex]
This can be written in scientific notation:
[tex]\[ E = 1.9878 \times 10^{-24} \, \text{J} \][/tex]
So, the energy of light with a frequency of [tex]\(3 \times 10^9\)[/tex] Hz is:
[tex]\[ 1.9878 \times 10^{-24} \, \text{J} \][/tex]
