Answer
The frequency of the photon: \( 6.59 \times 10^{14} \, \text{Hz} \)
The energy of the photon: \( 4.37 \times 10^{-19} \, \text{J} \).
Work Step by Step
To calculate the frequency of a photon, we can use the equation:
\[ \text{frequency} = \frac{\text{speed of light}}{\text{wavelength}} \]
The speed of light is approximately \( 3.00 \times 10^8 \, \text{m/s} \), and the wavelength is \( 455.5 \, \text{nm} = 455.5 \times 10^{-9} \, \text{m} \).
So, the frequency is:
\[ \text{frequency} = \frac{3.00 \times 10^8 \, \text{m/s}}{455.5 \times 10^{-9} \, \text{m}} \]
\[ \text{frequency} \approx 6.59 \times 10^{14} \, \text{Hz} \]
To calculate the energy of a photon, we can use the equation:
\[ \text{energy} = \text{Planck's constant} \times \text{frequency} \]
Planck's constant is approximately \( 6.626 \times 10^{-34} \, \text{J s} \).
So, the energy is:
\[ \text{energy} = 6.626 \times 10^{-34} \, \text{J s} \times 6.59 \times 10^{14} \, \text{Hz} \]
\[ \text{energy} \approx 4.37 \times 10^{-19} \, \text{J} \]
Therefore, the frequency of the photon is approximately \( 6.59 \times 10^{14} \, \text{Hz} \) and the energy of the photon is approximately \( 4.37 \times 10^{-19} \, \text{J} \).
