11.6 In order to escape from a metal the conduction electrons, whose motion within the metal is described by the free electron model, must overcome a potential barrier of height χ at the surface of the metal, i.e. an electron will escape only if its component of velocity normal to the surface exceeds (2χ/m)l/2. (m = mass of the electron.)

What is the current density of electrons emitted from the surface of the metal when the temperature T is such that χ – μ
kT? (μ = chemical potential of the electron gas.)