Question

Radiation in the infrared region of the electromagnetic spectrum is usually described in terms of wave numbers, ^~v = 1/lambda. A typical value of^~v in this region is 10^3 cm^-1. Calculate the values of v, lambda, and E for radiation with^~v = 10^3 cm^-1.

Answer 1

v= 3.0 ×10^13 Hz, lamda= 10^5 m, and E= 2.0 × 10^ -20 J.

Step-by-step explanation:

Okay, let us take some important hints out of the question;

The region is an Infrared region. Which falls into 700 nanometers (nm) to 1 millimeter (mm) region on the electromagnetic radiation spectrum.

We are to calculate for v, lamda ( λ= wavelength), E(energy).

So, let us go straight into the business. Shall we?

(1).

v = c/ λ. Where c= speed of light = approximately 3.0 × 10^8 metre per seconds, λ = wavelength= 10^3 cm^- (value from the question).

Therefore, v=( 3.0 × 10^8 metres per seconds) ÷ 10 cm^-.

There is a need to convert the cm^- to per metre.

===> v = (3.0 × 10^ 8 m/s) × 10 cm^- × [100 (cm/ 1m)] = 3.0 × 10^ 13 Hertz(Hz).

(2).

Calculate lamda, λ.

Lamda, λ= 1/ ^~v. (From the question).

Therefore, lamda, λ = 1/ 10^3 = 1× 10^-3 cm.

Converting centimeters (cm) to metres(m); 10^-3 × 10^-2 = 1×10^- 5 metres(m).

(3). Calculating the energy,E.

E= hv. Where h= Planck's constant.

Slotting in the values to change to JOULES, we have;

E= hv = hc^~v = 2.0 × 10^ -20 J.