To find the energy of a photon, we use the formula:
[tex]\[ E = h \times f \][/tex]
Where:
- [tex]\( E \)[/tex] is the energy of the photon
- [tex]\( h \)[/tex] is Planck's constant [tex]\( 6.63 \times 10^{-34} \, \text{J} \cdot \text{s} \)[/tex]
- [tex]\( f \)[/tex] is the frequency of the photon [tex]\( 7.3 \times 10^{-17} \, \text{Hz} \)[/tex]
Step-by-step solution:
1. Substitute the given values into the formula:
[tex]\[ E = (6.63 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (7.3 \times 10^{-17} \, \text{Hz}) \][/tex]
2. Calculate the energy:
[tex]\[ E = 6.63 \times 7.3 \times 10^{-34} \times 10^{-17} \][/tex]
Multiply the constants:
[tex]\[ 6.63 \times 7.3 = 48.399 \][/tex]
Combine the exponents of 10:
[tex]\[ 10^{-34} \times 10^{-17} = 10^{-51} \][/tex]
Therefore:
[tex]\[ E = 48.399 \times 10^{-51} \][/tex]
3. Express the energy using standard scientific notation:
[tex]\( 48.399 \times 10^{-51} \)[/tex] can be expressed as [tex]\( 4.8399 \times 10^{-50} \)[/tex], since [tex]\( 48.399 \times 10^{-51} \)[/tex] is equal to [tex]\( 4.8399 \times 10^{-50} \)[/tex].
4. Round the result to the nearest tenths place:
Rounding [tex]\( 4.8399 \)[/tex] to the nearest tenth gives [tex]\( 0.0 \)[/tex] as it rounds down.
So, the energy of the photon, to the nearest tenths place, is:
[tex]\[ 0.0 \times 10^{-50} \][/tex]
Thus, the energy of the photon is [tex]\( 0.0 \times 10^{-50} \)[/tex] d.
