What is the energy of a proton with a wavelength of 700.0 nm?
1 Answer
I got
Read the question carefully, and you should see it says proton... That is, a mass-ive particle with rest mass
Objects with a rest mass follow the de Broglie relation:
#lambda = h/(mv) = h/p#
and have kinetic energy given by
#K = 1/2 mv^2 = p^2/(2m)# ,where:
#h = 6.626 xx 10^(-34) "J"cdot"s"# is Planck's constant.#p = mv# is the linear momentum,#m# is the mass, and#v# is the speed.
Thus, its kinetic energy is related to the wavelength as follows:
#p = h/lambda#
#=># #color(green)(barul(|stackrel(" ")(" "K = (h//lambda)^2/(2m)" ")|))#
Thus, the kinetic energy is:
#K = ((6.626 xx 10^(-34) "kg"cdot"m"^2"/s")/(700.00 xx 10^(-9) "m"))^2/(2(1.673 xx 10^(-27) "kg"))#
#= 2.678 xx 10^(-28) "J"#
or
#color(blue)(K) = 2.678 xx 10^(-28) cancel"J" xx "1 eV"/(1.602 xx 10^(-19) cancel"J")#
#= color(blue)(1.672 xx 10^(-9) "eV")#
(We can only do this because protons have approx. the same charge magnitude as electrons. "Electron"-volt does not only apply to electrons.)