Question

Energy of an electromagnetic spectrum is 1.9875*10^-12 ergs. Its wave number in cm^-1 is

Answer 1

The energy of electromagnetic radiation is   . What is wavenumber in cm ?

We have the following data:

E (Energy of an Atom  ) =

h (Planck’s Constant) =

c (Speed of Light) ≈

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\: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}

hope this helps you