To determine the energy of a photon, we can use the equation:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\( 6.63 \times 10^{-34} \, J \cdot s \)[/tex]),
- [tex]\( f \)[/tex] is the frequency of the photon ([tex]\( 2.9 \times 10^{-16} \, Hz \)[/tex]).
Substituting the given values into the equation:
[tex]\[ E = (6.63 \times 10^{-34} \, J \cdot s) \cdot (2.9 \times 10^{-16} \, Hz) \][/tex]
[tex]\[ E = 6.63 \times 2.9 \times 10^{-34} \times 10^{-16} \, J \][/tex]
[tex]\[ E = 19.227 \times 10^{-50} \, J \][/tex]
[tex]\[ E = 1.9227 \times 10^{-49} \, J \][/tex]
Next, to express the energy to the nearest tenths place in terms of [tex]\( 10^{-49} \, J \)[/tex], we round [tex]\( 1.9227 \)[/tex] to the nearest tenth:
[tex]\[ E \approx 1.9 \times 10^{-49} \, J \][/tex]
Therefore, the energy of the photon is:
[tex]\[ \boxed{1.9 \times 10^{-49} \, J} \][/tex]
