Question

calculate wavenumber of the line having frequency 5 x 10^ 16 Hz

Answer 1

Wavelength = velocity / frequency
So, wave number
=1/ wavelength
= frequency / velocity
= 5×10^16 / 3 × 10^8
= 1. 67 × 10^8

Answer 2

Given:

Frequency = $5\times10^6 Hz$

To find:

Wave number = ?

Formula to be used:

• Frequency = $\frac{C}{\lambda}$
• Wave number = $\frac{1}{\lambda}$

Calculation:

To find the wave number wavelength is required. Therefore wavelength can be calculated using the following formula

Frequency = $\frac{speed of light}{wavelength}$ = $\frac{c}{\lambda}$

$5\times10^6 = \frac{3\times 10^8}{\lambda}$

$\lambda = \frac{3\times10^8}{6\times10^{16}} = \frac{1\times 10^{-8}}{2}$

∴ Wavelength  = $\frac{1\times 10^{-8}}{2}$

Substituting this value in the following formula gives the wave number

Wave number = $\frac{1}{\lambda}$

Wave number = $\frac{1}{\frac{1\times10^{-8}}{2} }$

Wave number = $\frac{2}{1\times 10^{-8}}$

Wave number = $2\times 10^8 m^{-1}$

Conclusion:

The wavenumber of the line having frequency $5\times10^6 Hz$ is calculated as $2\times 10^8 m^{-1}$.

Learn more about wave number

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Energy of a photon having wavenumber 1.00 cm^-1 is?

A) 6.62x10^-34

B) 1.99x10^-23

C) 6.62x10^-32

D) 6.62x10^-36

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