Question

The frequency of a wave is $6\times {10}^{15}{\text{s}}^{-1}$. Its wave number will be:

• A. ${10}^5{\text{cm}}^{-1}$
• B. $2\times {10}^7{\text{m}}^{-1}$
• C. $2\times {10}^7{\text{cm}}^{-1}$
• D. $2\times {10}^5{\text{m}}^{-1}$

Answer 1

The correct option is B $2\times {10}^7{\text{m}}^{-1}$

We know that,
$c=\lambda v$
where,
$c:$ speed of light;
$v:$ frequency;
$\lambda :$ wavelength
Therefore,
$\frac{1}{\lambda }=\frac{v}{c}$
Given, frequency $\left(v\right)=6\times {10}^{15}{\text{s}}^{-1}$
Hence,
wavenumber $\stackrel{-}{v}=\frac{1}{\lambda }=\frac{6\times {10}^{15}{\text{s}}^{-1}}{3\times {10}^8{\text{m s}}^{-1}}=2\times {10}^7{\text{m}}^{-1}$