QJEEM24Cha135: JEE Main 2024 Chemistry - Class 11 JEEM24Cha135 Solution: Wavenumber for a radiation having 5800 wavelength is The value…

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 $\mathrm{cm}^{-1}$ .

First, convert the given wavelength from angstroms ( $\mathop A\limits^o$ ) to centimeters (cm). We know that:

$1 \mathop A\limits^o = 10^{-8} \, \text{cm}$

Given wavelength is 5800 $\mathop A\limits^o$ :

$5800 \mathop A\limits^o = 5800 \times 10^{-8} \, \text{cm}$

Now calculate the wavenumber ( $\tilde{\nu}$ ) which is the reciprocal of the wavelength:

$\tilde{\nu} = \frac{1}{{5800 \times 10^{-8} \, \text{cm}}}$

Simplify the expression:

$\tilde{\nu} = \frac{1}{5800 \times 10^{-8} \, \text{cm}} = \frac{10^8}{5800} \, \mathrm{cm}^{-1}$

Now, divide the numerator by the denominator to calculate the precise value:

$\tilde{\nu} = \frac{10^8}{5800} \approx 1.724 \times 10^4 \, \mathrm{cm}^{-1}$

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:

$x = \frac{1.724 \times 10^4}{10} = 1724$

Thus, the integer answer for the value of $x$ is:

1724