Question

The energy of electromagnetic radiation is 19.875×10^-13ergs what is wavenumber in cm^-1

Answer 1

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The energy of electromagnetic radiation is 19.875×10^-13ergs what is wavenumber in cm ?

• We have the following data:

E (Energy of an Atom) = $19.875*10^{-13}\:ergs$

h (Planck’s Constant) = $6.625*10^{-27}\:ergs/s$

c (Speed of Light) ≈ $3*10^{10}\:cm/s$

λ (Wavenumber or Wavelength of Photon) = ? (in cm)

• We apply the data to the formula of Energy of an atom, we have:

$E = h*\dfrac{c}{\lambda}$

$19.875*10^{-13}\:ergs = 6.625*10^{-27}\:ergs/s*\dfrac{3*10^{10}\:m/s}{\lambda}$

$\lambda = \dfrac{6.625*10^{-27}\:ergs\!\!\!\!\!\!\!\!\!\!\!\!\!\dfrac{\hspace{0.8cm}}{~}/\diagup\!\!\!\!s*3*10^{10}\:cm/\diagup\!\!\!\!s}{19.875*10^{-13}\:ergs\!\!\!\!\!\!\!\!\!\!\!\!\!\dfrac{\hspace{0.8cm}}{~}}$

$\lambda = \dfrac{1.9875*10^{-16}\:cm}{19.875*10^{-13}}$

$\lambda = \dfrac{1.9875*10^{-16}\:cm}{19.875*10^{-13}}$

$\lambda = \dfrac{1.9875\:cm}{19.875}*10^{-16-(-13)}$

$\lambda = \dfrac{1.9875\:cm}{19.875}*10^{-16+13}$

$\lambda = 0.1\:cm*10^{-3}$

$\boxed{\boxed{\lambda = 1*10^{-4}\:cm}}\Longleftarrow(wavenumber)\:\:\:\:\:\:\bf\purple{\checkmark}$

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