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Chemistry Question on Structure of atom

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

Answer

The wavenumber (ν~\tilde{\nu}) is given by:
ν~=1λ,\tilde{\nu} = \frac{1}{\lambda},
where λ\lambda is the wavelength in cm.
Step 1: Convert wavelength to cm
λ=5800 A˚=5800×10−8 cm.\lambda = 5800 \, \text{\AA} = 5800 \times 10^{-8} \, \text{cm}.
Step 2: Calculate wavenumber
ν~=15800×10−8=15.8×10−5=17241 cm−1.\tilde{\nu} = \frac{1}{5800 \times 10^{-8}} = \frac{1}{5.8 \times 10^{-5}} = 17241 \, \text{cm}^{-1}.
Step 3: Express as x×10 cm−1x \times 10 \, \text{cm}^{-1}
17241 cm−1=1724×10 cm−1.17241 \, \text{cm}^{-1} = 1724 \times 10 \, \text{cm}^{-1}.

Explanation

Solution

The wavenumber (ν~\tilde{\nu}) is given by:
ν~=1λ,\tilde{\nu} = \frac{1}{\lambda},
where λ\lambda is the wavelength in cm.
Step 1: Convert wavelength to cm
λ=5800 A˚=5800×10−8 cm.\lambda = 5800 \, \text{\AA} = 5800 \times 10^{-8} \, \text{cm}.
Step 2: Calculate wavenumber
ν~=15800×10−8=15.8×10−5=17241 cm−1.\tilde{\nu} = \frac{1}{5800 \times 10^{-8}} = \frac{1}{5.8 \times 10^{-5}} = 17241 \, \text{cm}^{-1}.
Step 3: Express as x×10 cm−1x \times 10 \, \text{cm}^{-1}
17241 cm−1=1724×10 cm−1.17241 \, \text{cm}^{-1} = 1724 \times 10 \, \text{cm}^{-1}.