To find the energy of a photon given its frequency and Planck's constant, we use the formula:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\( h = 6.63 \times 10^{-34} \)[/tex] J·s),
- [tex]\( f \)[/tex] is the frequency of the photon ([tex]\( f = 7.3 \times 10^{-17} \)[/tex] Hz).
Step-by-step solution:
1. Multiply Planck's constant by the frequency to find the energy:
[tex]\[ E = (6.63 \times 10^{-34} \, \text{J·s}) \times (7.3 \times 10^{-17} \, \text{Hz}) \][/tex]
2. Perform the multiplication:
[tex]\[ E = 6.63 \times 7.3 \times 10^{-34} \times 10^{-17} \][/tex]
[tex]\[ E = 48.399 \times 10^{-51} \][/tex]
[tex]\[ E = 4.8399 \times 10^{-50} \, \text{J} \][/tex]
3. Express the energy in the form of [tex]\( 4.8399 \times 10^{-50} \, \text{J} \)[/tex].
4. Round the energy to the nearest tenths place in the format [tex]\( x \times 10^{-50} \)[/tex]:
[tex]\[ 4.8399 \approx 4.8 \][/tex]
Therefore, the energy of the photon, to the nearest tenths place, is:
[tex]\[ 4.8 \times 10^{-50} \, \text{J} \][/tex]
