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# Light of Intensity 10−5 W M−2 Falls on a Sodium Photo-cell of Surface Area 2 Cm2. Assuming that the Top 5 Layers of Sodium Absorb the Incident Energy, Estimate Time Required for Photoelectric Emission in the Wave-picture of Radiation. the Work Function for the Metal is Given to Be About 2 Ev. What is the Implication of Your Answer? - CBSE (Science) Class 12 - Physics

ConceptExperimental Study of Photoelectric Effect

#### Question

Light of intensity 10−5 W m−2 falls on a sodium photo-cell of surface area 2 cm2. Assuming that the top 5 layers of sodium absorb the incident energy, estimate time required for photoelectric emission in the wave-picture of radiation. The work function for the metal is given to be about 2 eV. What is the implication of your answer?

#### Solution

Intensity of incident light, I = 10−5 W m−2

Surface area of a sodium photocell, A = 2 cm2 = 2 × 10−4 m2

Incident power of the light, P = I × A

= 10−5 × 2 × 10−4

= 2 × 10−9 W

Work function of the metal,phi_0 = 2 eV

= 2 × 1.6 × 10−19

= 3.2 × 10−19 J

Number of layers of sodium that absorbs the incident energy, n = 5

We know that the effective atomic area of a sodium atom, Ae is 10−20 m2.

Hence, the number of conduction electrons in n layers is given as:

n' = n xx A/A_e

= 5 xx (2xx10^(-4))/10^(-20) = 10^17

The incident power is uniformly absorbed by all the electrons continuously. Hence, the amount of energy absorbed per second per electron is:

E = P/"n'"

= (2xx10^(-9))/10^17  =2 xx 10^(-26) "J/s"

Time required for photoelectric emission:

t = phi_0/E

= (3.2 xx 10^(-19))/(2xx10^(-26)) = 1.6 xx       10^7 s ~~ 0.507 "year"

The time required for the photoelectric emission is nearly half a year, which is not practical. Hence, the wave picture is in disagreement with the given experiment.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 11: Dual Nature of Radiation and Matter
Q: 30 | Page no. 410
Solution Light of Intensity 10−5 W M−2 Falls on a Sodium Photo-cell of Surface Area 2 Cm2. Assuming that the Top 5 Layers of Sodium Absorb the Incident Energy, Estimate Time Required for Photoelectric Emission in the Wave-picture of Radiation. the Work Function for the Metal is Given to Be About 2 Ev. What is the Implication of Your Answer? Concept: Experimental Study of Photoelectric Effect.
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