Question

What is (a) the wavelength of a 5.10-eV photon and (b) the de Broglie wavelength of a 5.10-eV electron?

Answer 1

Givendata:

Photon has energy = 5.0 eV

wavelength =?

E(photon) = 5.10eV =5.10*1.602*0^-19 joules = 8.1702*10^-19 J

E = h f = h c / (wavelength)
wavelength = hc/E

wavelength = (6.62X10^-34Js)(3 x 10^8m/s)/( 8.1702× 10^-19 joules)

wavelength =0.00243*10^-4meters =2.43*10^-7m

b) energy of an electron = 5.10eV =  8.1702× 10^-19 joules

λ = h /p --------------(1)
p = mv
p^2 = m^2 v^2
KE = E = 0.5mv^2
so E = p^2/2m
p = [2mE]^1/2 substitute in eq(1)

λ = h /[2mE]^1/2

λ = (6.62*10^-34) /((2*9.1*10^-31* 8.1702× 10^-19)^0.5 )
λ = 5.4288 * 10^-10 meter