Question

A silicon (Φ = 7.77 × 10^-19 J) surface is irradiated with UV radiation with a wavelength of 259 nm.
what is the ke of the emitted electrons, what is the speed of the emmited electrons, what is the wavelength of the emmited electrons

Answer 1

A) Work function of Silicon (WO) = hv_o

Therefore v_o = W_O/h = 7.77x10^-19J/ 6.626x10^-34J.sec

= 1.17x10¹⁴/sec

B) λ_o =c/v_o = 3x10⁸ / 1.17x10¹⁴ = 3.42x10^-7m

C) K.E of ejected electron = h(v-v_o) = hc(1/λ – 1/ λ_o)

=(6.626x10^-34J.secx3x10⁸m/sec) (1/259x10^-9 – 1/342x10^-9)m

=(6.626x3x10^-17) (9.4x10^-4)J

=18.7x10^-20J

We know that KE.=1/2 mv²

k.E = 1mv²/2 = 18.7x10^-20J

=9.1x10^-31Kg. v²/2 = 18.7x10^-20J

Or

v² = 41.1x10¹⁰m²s^-2

Or

v = 6.41x10⁵ms^-1

Wave length of the emitted electron =hc/KE

                                                         = 6.626x10^-34J.sec.x3x10⁸m/sec/(18.7x10^-20J)

                                                         = 1.06x10^-6m

Hence, the wavelength of the emitted electron is : 1.06x10^-6m