Calculate the wave number of photon whose energy is 6.626×10^-20 J?
1 Answer
Well, it depends on what you mean...
In physics and physical chemistry, the wave number is
#k = (2pi)/lambda# ,
the number of waves per meter. The energy of a photon is
#E = hnu = (hc)/lambda# where:
#h = 6.626 xx 10^(-34) "J"cdot"s"# is Planck's constant.#c = 2.998 xx 10^(8) "m/s"# is the speed of light.#lambda# is the wavelength in#"m"# .
Hence, the wavelength is:
#lambda = (hc)/E = (6.626 xx 10^(-34) cancel"J"cdotcancel"s" cdot 2.998 xx 10^8 "m"cancel"/s")/(6.626 xx 10^(-20) cancel"J")#
#= 2.998 xx 10^(-6) "m"#
and thus, the "wave number" is:
#color(blue)(k) = (2pi)/(2.998 xx 10^(-6) "m")#
#= color(blue)(2.096 xx 10^6 "waves/meter")#
In spectroscopic chemistry, the wavenumber is the frequency
#color(blue)(tildenu) = E/(hc) = (6.626 xx 10^(-20) cancel"J")/(6.626 xx 10^(-34) cancel"J"cdotcancel"s") xx cancel"s"/(2.998 xx 10^10 "cm")#
#= color(blue)(3.336 xx 10^3 "cm"^(-1))#
