a) What is the frequency of a photon of UV radiation ( = 2.00 x 10^-7 m)? When you input
large numbers such as those in this problem, then input the numbers with parenthesis so as
to obtain the correct answer. (b) Calculate the energy of a photon of UV radiation. When
you input large numbers such as those in this problem, then input the numbers with
parenthesis so as to obtain the correct answer. (C) What is the frequency of a photon of
infrared radiation ( = 1.083 x 10^-6 m)? When you input large numbers such as those in this
problem, then input the numbers with parenthesis so as to obtain the correct answer. (d)
Calculate the energy of a photon of infrared radiation. When you input large numbers such
as those in this problem, then input the numbers with parenthesis so as to obtain the correct
answer. (e) How many times greater is the energy of a photon of ultraviolet radiation than
the energy of an average photon of infrared radiation?
To find the frequency of a photon, we can use the equation:
Frequency (ν) = speed of light (c) / wavelength (λ)
a) Given the wavelength of UV radiation (λ = 2.00 x 10^-7 m), we can use the speed of light (c = 3.00 x 10^8 m/s) to calculate the frequency.
Frequency = (3.00 x 10^8 m/s) / (2.00 x 10^-7 m)
Frequency = 1.50 x 10^15 Hz
Therefore, the frequency of the photon of UV radiation is 1.50 x 10^15 Hz.
To calculate the energy of a photon, we can use the equation:
Energy (E) = Planck's constant (h) x frequency (ν)
b) Given the frequency of the UV radiation (ν = 1.50 x 10^15 Hz) and Planck's constant (h = 6.63 x 10^-34 J·s), we can calculate the energy.
Energy = (6.63 x 10^-34 J·s) x (1.50 x 10^15 Hz)
Energy = 9.94 x 10^-19 J
Therefore, the energy of a photon of UV radiation is 9.94 x 10^-19 J.
c) Similarly, to find the frequency of a photon of infrared radiation, we can use the same equation:
Frequency = (3.00 x 10^8 m/s) / (1.083 x 10^-6 m)
Frequency = 2.77 x 10^14 Hz
Therefore, the frequency of the photon of infrared radiation is 2.77 x 10^14 Hz.
d) To calculate the energy of a photon of infrared radiation, we can use the same equation:
Energy = (6.63 x 10^-34 J·s) x (2.77 x 10^14 Hz)
Energy = 1.83 x 10^-19 J
Therefore, the energy of a photon of infrared radiation is 1.83 x 10^-19 J.
e) To find the ratio of the energy of a photon of ultraviolet radiation to the energy of an average photon of infrared radiation, we can divide their energies:
Ratio = Energy of UV radiation / Energy of infrared radiation
Ratio = (9.94 x 10^-19 J) / (1.83 x 10^-19 J)
Ratio = 5.43
Therefore, the energy of a photon of ultraviolet radiation is 5.43 times greater than the energy of an average photon of infrared radiation.