Problem: Titanium metal requires a photon with a minimum energy of  6.94 x 10 - 19 J to emit electrons.If titanium is irradiated with light of 233 nm, what is the maximum possible kinetic energy of the emitted electrons?

We’re being asked to calculate the maximum possible kinetic energy of the emitted electrons if titanium is irradiated with light of 233 nm. When photons with enough energy hit the surface of a metal, electrons are emitted. This phenomenon is known as the Photoelectric Effect.

Total energy (ΔE) in photoelectric effect can be calculated using the following equation:

$\boxed{\mathbf{∆}\mathbf{E}\mathbf{=}{\mathbf{E}}_{\mathbf{work}\mathbf{ }\mathbf{function}}\mathbf{+}{\mathbf{E}}_{\mathbf{kinetic}\mathbf{ }\mathbf{energy}}}$

Where:

• ΔE is the total energy or the energy of the light/photon/radiation and can be calculated using the equation:

$\boxed{\mathbf{∆}\mathbf{E}\mathbf{=}\mathbf{h\nu }}$

E_{total energy} = J
h = Planck’s constant = 6.626x10^-34 J∙s
ν = frequency = Hz or s^-1

• E_{work function} is the work function or threshold frequency of the metal (minimum energy required to remove an electron from the metal)