Convert 850 nm wavelength into frequency, eV, wavenumber, joules and ergs.

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Question:

Convert 850 nm wavelength into frequency, eV, wavenumber, joules and ergs.

Answers

Answer:Frequency = [tex]3.5294\times 10^{14}s^{-1}[/tex]Wavenumber = [tex]1.1765\times 10^6m^{-1}[/tex]Energy = [tex]2.3365\times 10^{-19}J[/tex]Energy = 1.4579 eVEnergy = [tex]2.3365\times 10^{-12}erg[/tex]Explanation:As we are given the wavelength = 850 nmconversion used : [tex](1nm=10^{-9}m)[/tex]So, wavelength is  [tex]850\times 10^{-9}m[/tex]The relation between frequency and wavelength is shown below as:[tex]Frequency=\frac{c}{Wavelength}[/tex]Where, c is the speed of light having value = [tex]3\times 10^8m/s[/tex]So, Frequency is:[tex]Frequency=\frac{3\times 10^8m/s}{850\times 10^{-9}m}[/tex][tex]Frequency=3.5294\times 10^{14}s^{-1}[/tex]Wavenumber is the reciprocal of wavelength.  So,  [tex]Wavenumber=\frac{1}{Wavelength}=\frac{1}{850\times 10^{-9}m}[/tex][tex]Wavenumber=1.1765\times 10^6m^{-1}[/tex]Also,  [tex]Energy=h\times frequency[/tex]where, h is Plank's constant having value as [tex]6.62\times 10^{-34}J.s[/tex]So,  [tex]Energy=(6.62\times 10^{-34}J.s)\times (3.5294\times 10^{14}s^{-1})[/tex][tex]Energy=2.3365\times 10^{-19}J[/tex]Also,  [tex]1J=6.24\times 10^{18}eV[/tex]So,  [tex]Energy=(2.3365\times 10^{-19})\times (6.24\times 10^{18}eV)[/tex][tex]Energy=1.4579eV[/tex]Also,  [tex]1J=10^7erg[/tex]So,  [tex]Energy=(2.3365\times 10^{-19})\times 10^7erg[/tex][tex]Energy=2.3365\times 10^{-12}erg[/tex]

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