Question

A certain photochemical reaction requires an excitation energy of 126 kJ mol^-1 . To what values does this correspond in the following units: (A) frequency of light, (B) wave number, (C) wavelength in nanometers, and (D) electron volts?

Answer 1

Given that excitation energy = 126 kJ mol^-1

   E = 126 kJ mol^-1 = 126000 J/mol

Divide this energy with Avogadro number to get energy in J.

E = 126000 J mol^-1 / Avogadro number = 126000 J mol^-1 / 6.023 x 10²³ mol^-1

   = 20919.8 x 10^-23 J

E =  20919.8 x 10^-23 J

A) Frequency:

E = hv , v = frequency

v = E/h

=  20919.8 x 10^-23 J / 6.626 x 10^-34 J.s

= 3157.2 x 10¹¹ Hz

Therefore, frequency v =  3157.2 x 10¹¹ Hz

C)  

E = hc /λ , λ = wavelength

λ = hc/E

   = 6.626 x 10^-34 J.s x 3 x10⁸ m/s / 20919.8 x 10^-23 J

= 950 x 10^-9 m

= 950 nm

Therefore, wavelength =  950 nm

B)

wavenumber = 1/ wavelength

= 1/ 950 x 10^-9 m

= 0.00105 x 10⁹ m^-1

Therefore, wavenumber = 0.00105 x 10⁹ m^-1

D) 1 J = 6.24 x 10¹⁸ ev

E = 20919.8 x 10^-23 J

= 20919.8 x 10^-23 x 6.24 x 10¹⁸

   = 130539 x 10^-5 eV

E = 130539 x 10^-5 eV