Question #183533

Calculate the threshold wavelength, in nm, of a metal if that metal emits an electron with a kinetic energy of 6.32 x 10-19 J when illuminated with light that has a frequency of 1.97 x 1015 Hz. 


1
Expert's answer
2021-04-22T07:28:31-0400

KE=hcλWoKE=\dfrac{hc}{\lambda}-W_o

Wo=hνKEW_o=h\nu-KE

Wo=(6.63×1034×1.97×1015)(6.32×1019)W_o=(6.63\times10^{-34}\times1.97\times10^{15})-(6.32\times10^{-19})

Wo=6.74×1019 JW_o=6.74\times10^{-19}\space J


For threshold wavelength(λ)(\lambda) ,

hcλ=Wo\dfrac{hc}{\lambda}=W_o

λ=hcWo=6.63×1034×3×1086.74×1019\lambda=\dfrac{hc}{W_o}=\dfrac{6.63\times10^{-34}\times3\times10^8}{6.74\times10^{-19}}

λ=2.95×107 m\lambda=2.95\times10^{-7}\space m

λ=295 nm\lambda=295\space nm


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