# A mercury lamp is

Given:

The frequency, v of a wave with wavelength λ is given by,

v = c/λ …(1)

(c = speed of light = 3 × 108ms-1)

By using equation (1) we can find frequency for each case,

The equation for photo-electric effect is given as,

Φ0 = hv- eV0

We can rewrite this equation as,

V0 = …(2)

Where,

h = Planck’s constant

c = speed of light = 3 × 108m

λ = wavelength of light

e = charge on each electron = 1.6 × 10-19C

We find that the slope of the graph remains same,

Slope of the line =

From equation (2),

We can write,

Slope = h/e

h = e × slope

h =

h = 6.58 × 10-34 Js

From the same graph, we can infer that, threshold frequency of the metal is 5 × 1014 Hz

i.e. v0 = 5 × 1014Hz

Work function, Φ0 = hv0 …(2)

Where,

h = Plank’s constant = 6.57 × 10-34Js

v0 = threshold frequency

By plugging the data in equation (2), we get,

Φ0 = 6.57 × 10-34Js × 5 × 1014Hz

Φ0 = 3.28 × 10-19 J

Φ0 = 2eV

Hence, the work function of the metal is 2eV.

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