The energy required to remove an electron from a surface of a solid element is c

Question

The energy required to remove an electron from a surface of a solid element is called its work function. If a minimum of 413.0 kJ/mol is required to remove electrons from Ag atoms on a surface of a sample of silver, what is the maximum wavelength (lambda max) of light that can remove an electron from an Ag atom on this surface? If the same silver surface is irradiated with light of lambda = 147.0 nm, what is the maximum kinetic energy that a released electron could have? The released electron cannot have as much energy as the incident photon, because there is work done in order to release the electron from the atom.

Explanation / Answer

                       Energy requied to remove the electrons = 413.0kJ/mol
                  1 mol contains 6.023 x 1023 electrons.                Energyrequired to remove one electron = (413.0 kJ/mol/ 6.023 x1023 mol-1 )                                                                                = 68.57 x 10-23 kJ                           E = h c /                   68.57 x 10-20 J   = ( 6.625 x 10-34 J.sec x 3 x 108 m/s ) /                   wave length of the light used =  2.87 x 10-7 m                             1 mol contains 6.023 x 1023 electrons.                Energyrequired to remove one electron = (413.0 kJ/mol/ 6.023 x1023 mol-1 )                                                                                = 68.57 x 10-23 kJ                           E = h c /                   68.57 x 10-20 J   = ( 6.625 x 10-34 J.sec x 3 x 108 m/s ) /                   wave length of the light used =  2.87 x 10-7 m                                  The silver surface is irradiated with the light of = 147.0 nm                    Energy of photon =   h c /                                                     = (6.625 x 10-34 J.s) *(2.99 x108 m/s) / 147.0 x 10-9m                                                     = 1.347 x 10-18 J                      In photoelectric efect ,                 Energyirradiated =   work function + kineticenergy of ejected electron.                   1.347 x 10-18 J =   + (1/2) mV2 --------   1               The work function of the electron = (413.0 x103 J/mol ) / 6.023 x 1023mol-1                                                                   = 68.57 x 10-20 J                       Kinetic energy of the ejected electron =1.347 x 10-18 J   - 68.57 x 10-20J                                                                                   = 0.6613 x 10-18 J                                                                   = 68.57 x 10-20 J                       Kinetic energy of the ejected electron =1.347 x 10-18 J   - 68.57 x 10-20J                                                                                   = 0.6613 x 10-18 J                                       

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