Question

The work function of tungsten is 4.50 eV. Calculate the speed of the fastest electrons ejected from a tungsten surface when light whose photon energy is 5.80 eV shines on the surface.

Short answer

The speed of the fastest electron is 676 km/s.

Step-by-step solution

Describe the equation of photoelectric emission:

The equation of photoelectric emission is given by,

$hf=K_{max}+\Phi$ ….. (1)

Here, h is the Planck’s constant, f is frequency, is work function, and is the maximum kinetic energy.

Determine the speed of the fastest electrons ejected from a tungsten surface:

The energy of the photon is hf= 5.8 eV

Substitute 5.8 eV for hf, and 4.5 eV for $\varphi$in equation (1).

It is known that,

$K_{\max }=\frac{1}{2}m{v}_{\max }^2$

$v_{\max }=\sqrt{\frac{2K_{\max }}{m}}$ ….. (2)

Hence, the speed of the fastest electron is 676 km/s.