Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# When a Metal Plate is Exposed to a Monochromatic Beam of Light of Wavelength 400 Nm, a Negative Potential of 1.1 V is Needed to Stop the Photo Current. Find the Threshold Wavelength for the Metal. - Physics

Sum

When a metal plate is exposed to a monochromatic beam of light of wavelength 400 nm, a negative potential of 1.1 V is needed to stop the photo current. Find the threshold wavelength for the metal.

(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)

#### Solution

Given :-

Wavelength of light, λ = 400  "nm" = 400 xx 10^-9  "m"

Stopping potential, V_0 = 1.1 V

From Einstein's photoelectric equation,

(hc)/λ = (hc)/(λ_0) + eV_0,

where h = Planck's constant

c = speed of light

λ = wavelength of light

λ_0 = threshold wavelength

V_0 = stopping potential

On substituting the respective values in the above formula ,  we get :

(6.63 xx 10^-34 xx 3 xx 10^8)/(400 xx 10^-9) = (6.63 xx 10^-34 xx 3 xx 10^8)/λ_0 + 1.6 xx 10^-19 xx 1.1

⇒ 4.97 xx 10^-19 = (19.89 xx 10^-26)/λ_0 + 1.76 xx 10^-19

⇒ 4.97 = (19.89 xx 10^-7)/λ_0 + 1.76

⇒ (19.89 xx 10^-7)/λ_0  = 4.97 - 1.76 = 3.21

⇒ λ_0 = (19.89 xx 10^-7)/3.21

= 6.196 xx 10^-7  "m" = 620  "nm"

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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 20 Photoelectric Effect and Wave-Particle Duality
Q 18 | Page 365