14. Calculate the energy of a wave with the wavelength of 4.80 x 105 nm. What type of radiation is this?

The energy of the wave is 4.14 × 10⁻²² J

The radiation is an infrared radiation because its wavelength is within the infrared range

From the question,

We are to determine the energy of the wave that has a wavelength of 4.80 × 10⁵ nm.

From the formula

Where E is the energy

h is Planck's constant (h=6.626 × 10⁻³⁴ Js)

and is the frequency

But frequency, is given by

Where c is the speed of light (c = 3.0 × 10⁸ m/s)

and λ is the wavelength

Then, we can write that

From the question

λ = 4.80 × 10⁵ nm = 4.80 × 10⁵ × 10⁻⁹ m

λ = 4.80 × 10⁻⁴ m

∴ Energy of the wave is

E ≅ 4.14 × 10⁻²² J

Hence, the energy of the wave is 4.14 × 10⁻²² J

The radiation is an infrared radiation because its wavelength is within the infrared range

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4.1 * 10^-22 J

The wave belongs to the infra red portion of the electromagnetic spectrum.

Explanation:

From the formula;

E = hc/λ

We know that;

h= plank's constant = 6.6 * 10^-34 Js

c= speed of light = 3 * 10^8 m/s

λ = wavelength of the wave = 4.80 x 10^5 nm or 4.80 x 10^-4 m

Hence;

E= 6.6 * 10^-34 * 3 * 10^8/ 4.80 x 10^-4

E= 4.1 * 10^-22 J

The wave belongs to the infra red portion of the electromagnetic spectrum.