An infrared photon has a wavelength of 900 nm. An ultraviolet photon has a wavelength of 300 nm.
The energy of the ultraviolet photon is __________the infrared photon
The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. Therefore, the ultraviolet photon, which has a shorter wavelength, has a higher energy compared to the infrared photon.
Therefore, the energy of the ultraviolet photon is greater than the energy of the infrared photon.
To calculate the energy of a photon, we can use the equation:
E = hc/λ
Where:
E = energy of the photon
h = Planck's constant (6.626 x 10^-34 Js)
c = speed of light (2.998 x 10^8 m/s)
λ = wavelength of the photon
Let's calculate the energy of the infrared photon first:
E_infrared = (6.626 x 10^-34 Js) * (2.998 x 10^8 m/s) / (900 x 10^-9 m)
= 2.209 x 10^-19 J
Now, let's calculate the energy of the ultraviolet photon:
E_ultraviolet = (6.626 x 10^-34 Js) * (2.998 x 10^8 m/s) / (300 x 10^-9 m)
= 6.622 x 10^-19 J
Comparing the energies:
The energy of the ultraviolet photon (6.622 x 10^-19 J) is higher than the energy of the infrared photon (2.209 x 10^-19 J).
To determine the energy of the photons, you can use the equation:
Energy (E) = Planck's constant (h) * Speed of light (c) / Wavelength (λ)
where Planck's constant (h) is approximately 6.626 x 10^-34 joule-seconds, the speed of light (c) is approximately 3 x 10^8 meters per second, and the wavelength (λ) is given in meters.
Let's calculate the energies of the given photons:
For the infrared photon with a wavelength of 900 nm (0.9 μm):
E_infrared = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (0.9 x 10^-6 m)
≈ 2.207 x 10^-19 joules
For the ultraviolet photon with a wavelength of 300 nm (0.3 μm):
E_ultraviolet = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (0.3 x 10^-6 m)
≈ 6.626 x 10^-19 joules
Comparing the energies:
E_ultraviolet / E_infrared ≈ (6.626 x 10^-19 J) / (2.207 x 10^-19 J)
≈ 2.999
Therefore, the energy of the ultraviolet photon is approximately 3 times greater than the energy of the infrared photon.