Question

Which wavelength of light (in nanometers) is emitted if an electron moves from the conduction band to the valence band in a sample of the ceramic silicon nitride? (Note that the ceramic silicon nitride has a band gap of 5.0 eV .)

Express the wavelength to two decimal places.

Answer 1

energy gap E= 5 eV = 5 x 1.602 x 10^-19 J = 8.01 x 10^-19 J

we use relation E = h c / lamda to find out lamda ( wavelength)

where h = planks constant = 6.625 x 10^-34 Js ,

c= speed of light = 3 x 10^8 m/s

Now 8.01 x 10^-19 J = ( 6.625 x 10^-34 Js) ( 3 x 10^8 m/s) / ( lamda)

lamda = 248 x 10^-9 m

         = 248 nm         

Thus wavelength corresponding to energy gap = 248 nm is wavelength of light emitted if electron moves from one band to other