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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

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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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