To determine 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, and [tex]\( f \)[/tex] is the frequency of the photon.
1. Write down the given values:
- Frequency [tex]\( f = 3.6 \times 10^{15} \, \text{Hz} \)[/tex]
- Planck's constant [tex]\( h = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s} \)[/tex]
2. Substitute these values into the formula:
[tex]\[ E = (6.63 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.6 \times 10^{15} \, \text{Hz}) \][/tex]
3. Multiply the numerical parts:
[tex]\[ 6.63 \times 3.6 = 23.868 \][/tex]
4. Multiply the exponential parts:
[tex]\[ 10^{-34} \times 10^{15} = 10^{-34+15} = 10^{-19} \][/tex]
5. Combine the results:
[tex]\[ E = 23.868 \times 10^{-19} \][/tex]
We can express this in scientific notation:
[tex]\[ E = 2.3868 \times 10^{-18} \, \text{J} \][/tex]
Rounding to the appropriate significant figures:
[tex]\[ E \approx 2.4 \times 10^{-18} \, \text{J} \][/tex]
6. Compare this result to the given choices:
- [tex]\( 1.8 \times 10^{-49} \, \text{J} \)[/tex]
- [tex]\( 2.4 \times 10^{-19} \, \text{J} \)[/tex]
- [tex]\( 1.8 \times 10^{-18} \, \text{J} \)[/tex]
- [tex]\( 2.4 \times 10^{-18} \, \text{J} \)[/tex]
The correct answer is:
[tex]\[ \boxed{2.4 \times 10^{-18} \, \text{J}} \][/tex]
