Question

Wavenumber for a radiation having $5800 \, \mathring{A}$ wavelength is $x \times 10 \, \text{cm}^{-1}$. The value of $x$ is _________

Answer 1

Correct Answer: 1724

The wavenumber ($\tilde{\nu}$) is given by:
\[ \tilde{\nu} = \frac{1}{\lambda}, \]
where $\lambda$ is the wavelength in cm.
Step 1: Convert wavelength to cm
\[ \lambda = 5800 \, \text{\AA} = 5800 \times 10^{-8} \, \text{cm}. \]
Step 2: Calculate wavenumber
\[ \tilde{\nu} = \frac{1}{5800 \times 10^{-8}} = \frac{1}{5.8 \times 10^{-5}} = 17241 \, \text{cm}^{-1}. \]
Step 3: Express as $x \times 10 \, \text{cm}^{-1}$
\[ 17241 \, \text{cm}^{-1} = 1724 \times 10 \, \text{cm}^{-1}. \]