Question

In: Physics

When 210 nm light falls on a metal, the current through a photoelectric circuit is brought...

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.

Solutions

Expert Solution

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.


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