Question

frequency of radiation having a wave number of 2 into 10 power 14 cm will be

Answer 1

if correct

if not then sorry

Answer 2

The frequency of radiation having wave number 2 × 10¹⁴ cm⁻¹, will be 6 × 10²⁴ s⁻¹.

Given,

The wave number of particular radiation = 2 × 10¹⁴ cm⁻¹.

To find,

Frequency of this radiation.

Solution,

A wave number can be defined as the spatial frequency of a wave. The wave number denotes the number of waves per unit distance and, is measured in cm⁻¹, usually.

It is given by the relation

$\bar \nu = \frac{1}{\lambda} \hfill ...(1)$

where,

$\bar \nu$ = wave number,

λ = wavelength.

We know that the frequency is given as

$\nu = \frac{c}{\lambda} \hfill ...(2)$

where c is the velocity of light.

From (1) and (2), we can see that

$\nu =c \bar \nu$

Here,

wave number = 2 × 10¹⁴ cm⁻¹ = 2 × 10¹⁶ m⁻¹, and as c = 3 × 10⁸ m/s.

Thus,

$\nu = 3 \times 10^{8} \times 2 \times 10^{16}$

$\implies \nu = 6 \times 10^{24}$ s⁻¹.

Therefore, the frequency of radiation having wave number 2 × 10¹⁴ cm⁻¹, will be 6 × 10²⁴ s⁻¹.

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