Question

When light of wavelength 420 nm strikes a metal surface, photoelectrons having a kinetic energy of 6.0 x 10^-20 J are released.

a) What is the energy needed to remove an electron from the metal atom?

b) How much total energy would be needed to remove an electron from a mole of these metal atoms?

c) How many moles of photons would be required in part (b)?

Answer 1

use, for energy when wavelength is given

E = (h*C)/(wavelength)

value of planck constant h = 6.6*10^-34 (J*s)

wavelength = 420 nm

= 420*10^-9 m

= 42*10^-8 m

E = (6.6*10^-34*3*10⁸)/(42*10^-8)

E = (19.8*10^-26)/(42*10^-8)

E = (0.47*10^-18) J

E = (47*10^-20) J

a)

use,

K.E = E - (energy required)

6*10^-20 = 47*10^-20 - (energy required)

energy required = 47*10^-20 - 6*10^-20

energy required =41*10^-20 J

^b)

^{1 mole of any substances has 6.02*10 23 atom}

1 atom require 41*10^-20 J

6.02*10²³ atom require (6.02*10²³ *41*10^-20) J

energy require for 1 mole of atom = (6.02*10²³ *41*10^-20) J

energy require for 1 mole of atom = (246.8*10³) J

c)

n*(energy of one photon) =  (246.8*10³) J

n*E =  (246.8*10³) J

n*(47*10^-20) J = (246.8*10³) J

n = 5.25*10²³