Wavenumber for a radiation having 5800 $\mathop A\limits^o$ wavelength is $x \times 10 \mathrm{~cm}^{-1}$ The value of $x$ is ________. (Integer answer)

<p>The wavenumber of a radiation is defined as the number of wavelengths per unit distance and is the reciprocal of the wavelength. Wavenumber is commonly represented in units of $\mathrm{cm}^{-1}$.</p> <p>First, convert the given wavelength from angstroms ($\mathop A\limits^o$) to centimeters (cm). We know that:</p> <p>$1 \mathop A\limits^o = 10^{-8} \, \text{cm}$</p> <p>Given wavelength is 5800 $\mathop A\limits^o$:</p> <p>$5800 \mathop A\limits^o = 5800 \times 10^{-8} \, \text{cm}$</p> <p>Now calculate the wavenumber ($\tilde{\nu}$) which is the reciprocal of the wavelength:</p> <p>$\tilde{\nu} = \frac{1}{{5800 \times 10^{-8} \, \text{cm}}}$</p> <p>Simplify the expression:</p> <p>$$\tilde{\nu} = \frac{1}{5800 \times 10^{-8} \, \text{cm}} = \frac{10^8}{5800} \, \mathrm{cm}^{-1}$$</p> <p>Now, divide the numerator by the denominator to calculate the precise value:</p> <p>$\tilde{\nu} = \frac{10^8}{5800} \approx 1.724 \times 10^4 \, \mathrm{cm}^{-1}$</p> <p>Here, it is given that the wavenumber is in the form of $x \times 10 \, \mathrm{cm}^{-1}$, so $x$ would be the value we calculated divided by 10:</p> <p>$x = \frac{1.724 \times 10^4}{10} = 1724$</p> <p>Thus, the integer answer for the value of $x$ is:</p> <p><strong>1724</strong></p>