JEE Main 2024 — Structure Of Atom Question with Solution

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 ($$\stackrel{o}{A}$$) to centimeters (cm). We know that:

$$1\stackrel{o}{A}=10^{-8}\text{cm}$$

Given wavelength is 5800 $$\stackrel{o}{A}$$:

$$5800\stackrel{o}{A}=5800\times 10^{-8}\text{cm}$$

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