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
9 times smaller than
the same as
3 times larger than
9 times larger than
3 times smaller than
The energy of a photon is directly proportional to its frequency, and inversely proportional to its wavelength. Since ultraviolet light has a shorter wavelength than infrared light, the ultraviolet photon will have a higher frequency and therefore higher energy.
Therefore, the energy of the ultraviolet photon is 9 times larger than the infrared photon.
To determine the energy of each photon, we can use the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (3.00 × 10^8 m/s), and λ is the wavelength of the photon in meters.
Let's convert the given wavelengths to meters before using the formula:
Infrared photon wavelength: 900 nm = 900 × 10^-9 m
Ultraviolet photon wavelength: 300 nm = 300 × 10^-9 m
Using the equation E = hc/λ, we can calculate the energy for each photon:
For the infrared photon:
E_infrared = (6.626 × 10^-34 J·s × 3.00 × 10^8 m/s) / (900 × 10^-9 m)
E_infrared = 1.10 × 10^-19 J
For the ultraviolet photon:
E_ultraviolet = (6.626 × 10^-34 J·s × 3.00 × 10^8 m/s) / (300 × 10^-9 m)
E_ultraviolet = 6.63 × 10^-19 J
Comparing the energies:
E_ultraviolet = 6.63 × 10^-19 J
E_infrared = 1.10 × 10^-19 J
The energy of the ultraviolet photon is 6.63 × 10^-19 J, which is 6 times larger than the infrared photon. Therefore, the correct answer is:
- The energy of the ultraviolet photon is 6 times larger than the infrared photon.
The energy of a photon is directly proportional to its frequency, and inversely proportional to its wavelength. The higher the frequency, the higher the energy, and the shorter the wavelength, the higher the frequency.
Given that the infrared photon has a longer wavelength (900 nm) compared to the ultraviolet photon (300 nm), we can conclude that the energy of the ultraviolet photon is 3 times larger than the energy of the infrared photon.
The correct answer is: 3 times larger than