To find the energy of a photon that emits light of a given frequency, we can use the equation derived from Planck's theory:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\(6.626 \times 10^{-34} \, \text{Js}\)[/tex]),
- [tex]\( f \)[/tex] is the frequency of the photon.
Given the frequency [tex]\( f = 7.21 \times 10^{14} \, \text{Hz} \)[/tex], we can substitute this into the equation along with Planck's constant to find the energy [tex]\( E \)[/tex].
Substituting the given values:
[tex]\[ E = (6.626 \times 10^{-34} \, \text{Js}) \times (7.21 \times 10^{14} \, \text{Hz}) \][/tex]
Carrying out this multiplication,
[tex]\[ E \approx 4.777346 \times 10^{-19} \, \text{J} \][/tex]
From the provided options, the answer that most closely matches this calculated value is:
B. [tex]\( 4.78 \times 10^{-19} \, \text{J} \)[/tex]
Therefore, the energy of a photon that emits light of frequency [tex]\( 7.21 \times 10^{14} \, \text{Hz} \)[/tex] is:
[tex]\[ \boxed{4.78 \times 10^{-19} \, \text{J}} \][/tex]
