To solve this question, we need to calculate the energy of a photon using its wavelength. We can use the formula for the energy of a photon:
[tex]\[ E = \frac{h \cdot c}{\lambda} \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\( 6.62607015 \times 10^{-34} \)[/tex] Joule·seconds),
- [tex]\( c \)[/tex] is the speed of light in a vacuum ([tex]\( 3 \times 10^8 \)[/tex] meters/second),
- [tex]\( \lambda \)[/tex] is the wavelength of the photon.
Given:
[tex]\[ \lambda = 9 \times 10^{-8} \text{ m} \][/tex]
1. First, we need to understand what each term represents and plug in the known values:
- [tex]\( h = 6.62607015 \times 10^{-34} \, \text{Joule·seconds} \)[/tex]
- [tex]\( c = 3 \times 10^8 \, \text{m/s} \)[/tex]
- [tex]\( \lambda = 9 \times 10^{-8} \, \text{m} \)[/tex]
2. Now substitute these values into the formula:
[tex]\[ E = \frac{6.62607015 \times 10^{-34} \cdot 3 \times 10^8}{9 \times 10^{-8}} \][/tex]
3. Calculate the numerator:
[tex]\[ 6.62607015 \times 10^{-34} \cdot 3 \times 10^8 = 1.987821045 \times 10^{-25} \, \text{Joule·meters} \][/tex]
4. Now divide the result by the given wavelength:
[tex]\[ E = \frac{1.987821045 \times 10^{-25}}{9 \times 10^{-8}} \][/tex]
5. Perform the division:
[tex]\[ E = 2.20869005 \times 10^{-18} \, \text{J} \][/tex]
Therefore, the energy of a photon with a wavelength of [tex]\( 9 \times 10^{-8} \)[/tex] meters is approximately:
[tex]\[ \boxed{2.21 \times 10^{-18} \, \text{J}} \][/tex]
So, the correct answer is:
D. [tex]\( 2.21 \times 10^{-18} \, \text{J} \)[/tex]
