To calculate the energy of a photon based on its frequency, we can use Planck's 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]\( 6.63 \times 10^{-34} \)[/tex] J·s),
- [tex]\( f \)[/tex] is the frequency of the photon ([tex]\( 3.6 \times 10^{15} \)[/tex] Hz).
Let's go through the steps to calculate the energy:
1. Identify the given values:
- Frequency ([tex]\( f \)[/tex]) = [tex]\( 3.6 \times 10^{15} \)[/tex] Hz
- Planck's constant ([tex]\( h \)[/tex]) = [tex]\( 6.63 \times 10^{-34} \)[/tex] J·s
2. Plug the values into Planck's equation:
[tex]\[ E = (6.63 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.6 \times 10^{15} \, \text{Hz}) \][/tex]
3. Perform the multiplication of the constants:
[tex]\[ E = 6.63 \times 3.6 \times 10^{-34+15} \][/tex]
[tex]\[ E = 23.868 \times 10^{-19} \][/tex]
4. Adjust the numerical value to fit into standard scientific notation:
[tex]\[ E = 2.3868 \times 10^{-18} \, \text{J} \][/tex]
Considering significant figures (since the given data are typically to 2-3 significant figures):
[tex]\[ E \approx 2.387 \times 10^{-18} \, \text{J} \][/tex]
Considering the options provided, the nearest value is:
[tex]\[ E = 2.4 \times 10^{-18} \, \text{J} \][/tex]
Thus, the correct answer is:
[tex]\[ 2.4 \times 10^{-18} \, \text{J} \][/tex]
