To determine the energy of a photon with a wavelength of [tex]\( 9 \times 10^{-8} \)[/tex] meters, we use the formula for the energy of a photon in terms of its wavelength:
[tex]\[ E = \frac{hc}{\lambda} \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is the Planck constant ([tex]\( 6.62607015 \times 10^{-34} \)[/tex] J⋅s),
- [tex]\( c \)[/tex] is the speed of light in a vacuum ([tex]\( 3.0 \times 10^8 \)[/tex] m/s),
- [tex]\( \lambda \)[/tex] is the wavelength of the photon.
Given:
- [tex]\( \lambda = 9 \times 10^{-8} \)[/tex] meters,
- [tex]\( h = 6.62607015 \times 10^{-34} \)[/tex] J⋅s,
- [tex]\( c = 3.0 \times 10^8 \)[/tex] m/s.
Now, substituting these values into the formula:
[tex]\[ E = \frac{(6.62607015 \times 10^{-34} \, \text{J⋅s}) \times (3.0 \times 10^8 \, \text{m/s})}{9 \times 10^{-8} \, \text{m}} \][/tex]
Performing the calculation yields:
[tex]\[ E \approx 2.2086900499999997 \times 10^{-18} \, \text{J} \][/tex]
Thus, the energy of the photon is approximately [tex]\( 2.21 \times 10^{-18} \)[/tex] joules.
Therefore, the correct answer is:
A. [tex]\( 2.21 \times 10^{-18} \)[/tex] J
