Answer: the wavelength of the photon is approximately 3.58 × 10^-18 meters.
Explanation: where E is the energy of the photon, h is Planck's constant, f is the frequency of the photon, c is the speed of light, and λ is the wavelength of the photon.
We can rearrange this equation to solve for the wavelength:
λ = hc/E
where all variables have their previously defined meanings.
First, we need to convert the energy from joules to electronvolts (eV), which is a more commonly used unit for photon energy:
8.87 × 10^-28 J = 8.87 × 10^-28 J / 1.602 × 10^-19 J/eV = 5.53 × 10^-10 eV
Next, we can substitute the given values into the equation:
λ = (6.626 × 10^-34 J s) × (2.998 × 10^8 m/s) / (5.53 × 10^-10 eV)
Simplifying, we get:
λ = 3.580 × 10^-18 m
Finally, we can express the wavelength in scientific notation with three significant figures:
λ = 3.58 × 10^-18 m