The rays of the Sun that cause tanning and burning are in the ultraviolet portio

Question

The rays of the Sun that cause tanning and burning are in the ultraviolet portion of the electromagnetic spectrum. These rays are categorized by wavelength: So-called UV-A radiation has wavelengths in the range of 320-380 nm, whereas UV-B radiation has wavelengths in the range of 290-320 nm.

(a) Calculate the energy of a mole of 360 nm photons. (answer in Kj/mol)

An AM radio station broadcasts at 1140 kHz, and its FM partner broadcasts at 101.0 MHz. Calculate and compare the energy of photons emitted by these radio stations.

(b) EFM / EAM

Explanation / Answer

a)

Energy of a photon is given by following expression:

E = hc/

Where, h = plank’s constant (6.63 x 10-34 m2kg/s)

c = velocity of light (3 x 108 m/s)

= wavelength (360 nm)

E = (6.63 x 10-34 m2kg/s) x (3 x 108 m/s) / (360 nm)

Convert nm into m by multiplying 10-9

E = (6.63 x 10-34 m2kg/s) x (3 x 108 m/s) / (360 x 10-9 m)

E = 0.05525 x 10-17 m2kg/s2

E = 0.05525 x 10-20 kJ

Therefore, energy of 1 photon is 0.05525 x 10-20 kJ. One mole of photons contain 6.026 x 1023 photons. Therefore calculate energy of one mole of photons as follows:

Energy of 1 mole of photons = 6.026 x 1023 mol-1 x 0.05525 x 10-20 kJ

Energy of 1 mole of photons = 0.3329 x 103 kJ mol-1

Energy of 1 mole of photons = 332.9 kJ mol-1

Therefore, energy of a mole of 360 nm photons is 332.9 kJ mol-1.

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b)

Expression of energy of photon in terms of frequency is given as follows:

E = hv

Where, v = frequency (Hz)

Calculate energy of AM photon having frequency 1140 kHz

E = (6.63 x 10-34 m2kg/s) (1140 kHz)

Convert kHz into Hz

E = (6.63 x 10-34 m2kg/s) (1140 x 103 Hz)

E = 7558.2 x 10-31 J

Therefore, energy of a photon from AM wave is 7558.2 x 10-31 J

Similarly, calculate energy of photon of FM station having frequency 101.0 MHz.

E = (6.63 x 10-34 m2kg/s) (101.0 MHz)

E = (6.63 x 10-34 m2kg/s) (101.0 x 106 Hz)

E = 669.63 x 10-28 J

Therefore, energy of a photon from FM wave is 669.63 x 10-28 J

Ratio of energy of energy of FM photon (EFM) to energy of AM photon (EAM) is calculated as follows:

EFM/EAM = (669.63 x 10-28 J) / (7558.2 x 10-31 J)

EFM/EAM = 88.6

Therefore, Ratio of energy of energy of FM photon (EFM) to energy of AM photon (EAM) is 88.6

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