In: Physics
When 210 nm light falls on a metal, the current through a photoelectric circuit is brought to zero at a stopping voltage of 1.54 V . What is the work function of the metal? Express your answer using three significant figures.
Given,
wavelength of light, = 210 nm = 210x10–9 m
stopping voltage, Vo = 1.54V
The stopping voltage is the voltage at which the electrons with maximum kinetic energy are stopped, and as a result, the photoelectric current in the circuit, is brought to zero.
Therefore, Kmax = eVo
The photoelectric equation is, Kmax = h – = (hc/) –
Here, h is the Planck's constant (h = 6.625x10–34 Js)
is the work function of the metal.
is the frequency of the light, and
c is the speed of light ; c = 3x108m/s
So, from Kmax = (hc/) –
= (hc/) – Kmax
= (hc/) – eVo
= (6.625x10–34 x 3x108/210x10–9) – 1.6x10–19x1.54 ( charge of electron = 1.6x10–19C)
= (19.875x10–17/210) – 2.464x10–19
= 0.09464x10–17– 2.464x10–19
= 9.464x10–19– 2.464x10–19
= 7x10–19 J
= (7/1.6x10–19)x10–19 eV
= 4.375 eV
= 4.38 eV
So, the work function of the metal is 4.38 eV.