Question

Calculate the frequency and wave number of yellow radiation having wavelength $5800\AA$?

Answer 1

Step 1: Given data

Wavelength of radiation$=5800\AA$

$=5800\times {10}^{-10}\text{m}$

Step 2: To find

We have to find the frequency and the wave number.

Step 3: Determine the wave number

The given wavelength is,

$$\begin{gathered} \mathrm{\lambda }=5800\AA \\ =5800\times {10}^{-10}\mathrm{m} \end{gathered}$$

Thus, the wave number is,

$$\begin{gathered} \overline{\mathrm{v}}=\frac{1}{\mathrm{\lambda }} \\ \overline{\mathrm{v}}=\frac{1}{5800\times {10}^{-10}} \\ \overline{\mathrm{v}}=1.724\times {10}^6{\mathrm{m}}^{-1} \\ \overline{\mathrm{v}}=1.724\times {10}^4{\mathrm{cm}}^1 \end{gathered}$$

Step 4: Determine the frequency
$$\begin{gathered} \mathrm{V}=\frac{\mathrm{c}}{\mathrm{\lambda }} \\ \mathrm{V}=\frac{3\times {10}^8{\mathrm{ms}}^{-1}}{5800\times {10}^{-10}\mathrm{m}} \\ \mathrm{V}=5.172\times {10}^{-14}{\mathrm{s}}^{-1} \end{gathered}$$

Thus, the frequency and wave number of yellow radiation is $\mathrm{V}=5.172\times {10}^{-14}{\mathrm{s}}^{-1}$ and $\overline{\mathrm{v}}=1.724\times {10}^4{\mathrm{cm}}^1$.