Question #18492
1 Answer
#DeltaE_("vis") = (5.094 - 2.838) xx 10^(-19)color(white)(.)"J"#
#Deltanu_("vis") = (7.687 - 4.283) xx 10^(14)color(white)(.)"s"^(-1)" or Hz"# for the visible light range of
#390 - "700 nm"# .
Visible light is known to be in the region
The relationship between energy and frequency is given by the equation for energy
#bb(E = hnu)# ,where
#h = 6.626 xx 10^(-34) "J"cdot"s"# is Planck's constant, and#nu# is the frequency of the light in#"s"^(-1)# .
And the relationship between frequency
#bb(nu = c/lambda)# ,with
#lambda# in#"m"# and#c = 2.998 xx 10^(8)# #"m/s"# .
Or, combined, we get
#bb(E = (hc)/lambda)# .
#E = (hc)/lambda = ((6.626 xx 10^(-34) "J"cdot"s")(2.998 xx 10^(8) "m/s"))/(390 xx 10^(-9) "m")#
#= ul(5.094 xx 10^(-19)color(white)(.)"J")#
Likewise, the upper wavelength bound of
#color(blue)(barul|stackrel(" ")(" "DeltaE_("vis") = (5.094 - 2.838) xx 10^(-19)color(white)(.)"J"" ")|)#
#nu = E/h = c/lambda#
#= (2.998 xx 10^(8) "m/s")/(390 xx 10^(-9) "m")#
#= ul(7.687 xx 10^(14)color(white)(.)"s"^(-1)" or Hz")#
Likewise, the upper wavelength bound of
#color(blue)(barul|stackrel(" ")(" "Deltanu_("vis") = (7.687 - 4.283) xx 10^(14)color(white)(.)"s"^(-1)" or Hz"" ")|)#