Answer:
a
[tex]\lambda_{long} = 288.5 \ nm[/tex]
b
The velocity is  [tex]v = 3.7 *0^{5} \ m/s[/tex]
Explanation:
From the question we are told that
  The work function of Zinc is  [tex]W = 4.3 eV[/tex]
Generally the work function can be mathematically represented as
   [tex]E_o = \frac{hc}{\lambda_{long}}[/tex]
=> Â [tex]\lambda_{long} = \frac{hc}{E_o}[/tex]
Here  h is the Planck constant with the value  [tex]h = 4.1357 * 10^{-15} eV s[/tex]
 and c is the speed of light with value  [tex]c = 3.0 *10^{8} \ m/s[/tex]
So
   [tex]\lambda_{long} = \frac{4.1357 * 10^{-15} * 3.0 *10^{8}}{4.3}[/tex]
=> Â [tex]\lambda_{long} = 2.885 *10^{-7} \ m[/tex]
=> Â [tex]\lambda_{long} = 288.5 \ nm[/tex]
Generally the kinetic energy of the emitted electron is mathematically represented as
   [tex]K = E -E_o[/tex]
Here  E is the energy of the photon that strikes the surface
So
  [tex]E- E_o = \frac{1}{2} m * v^2[/tex]
Here m is the mass of electron with value  [tex]m = 9.11*10^{-31 } \ kg[/tex]
Generally  [tex]1 ev = 1.60 *10^{-19} \ J[/tex]
=> Â [tex]v = \sqrt{ \frac{2 (E - E_o ) }{ m } }[/tex]
=> Â Â [tex]v = \sqrt{ \frac{2 (4.7 - 4.3 )* 1.60 *10^{-19} }{ 9.11 *10^{-31} } }[/tex]
=> Â Â [tex]v = 3.7 *0^{5} \ m/s[/tex]
 Â
