Question 51

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


Correct Answer: 1724

We need to find the wavenumber for radiation with wavelength $$5800 \text{ \AA}$$. Since the wavenumber is defined as $$\bar{\nu} = \frac{1}{\lambda}$$, we first convert the wavelength to centimeters, giving $$\lambda = 5800 \text{ \AA} = 5800 \times 10^{-8} \text{ cm} = 5.8 \times 10^{-5} \text{ cm}$$.

Substituting this into the expression for the wavenumber yields $$\bar{\nu} = \frac{1}{5.8 \times 10^{-5}} = \frac{10^5}{5.8} = 17241.4 \text{ cm}^{-1}$$.

Since $$\bar{\nu} = x \times 10 \text{ cm}^{-1}$$, it follows that $$x = \frac{17241.4}{10} = 1724.14$$.

Therefore, rounding to the nearest integer gives $$x = \boxed{1724}$$.

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