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

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