LM004 for online chem hw?

Question

LM004

It takes 208.4 kJ of energy to remove 1 mole of electrons from an atom on the surface of rubidium metal. What is the maximum wavelength (in nm) of light capable of removing a single electron from an atom on the surface of rubidium metal?

Answer 1

One mole of electrons is Na = 6.023x10^23 electrons, so it takes:

E = 208.4x10^3/6.023x10^23 J = 3.46x10^(-19) J to remove 1 electron.

E = h*f, where E the energy of a photon, h = 6.63x10^(-34) J*s the Planck's constant and f the frequency of light. Solving for f:

f = E/h, f = 3.46x10^(-19)/6.63x10^(-34), f = 5.22x10^14 Hz

But:

c = λ*f, where c = 3x10^8 m/s the speed of light and λ the wavelength. Solving for λ:

λ = c/f, λ = 3x10^8/5.22x10^14, λ = 5.75x10^(-7) m, or

λ = 575 nm