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Question -

Light of intensity 10−5 W m−2 fallson a sodium photo-cell of surface area 2 cm2. Assuming that the top5 layers of sodium absorb the incident energy, estimate time required forphotoelectric emission in the wave-picture of radiation. The work function forthe metal is given to be about 2 eV. What is the implication of your answer?



Answer -

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

Workfunction of the metal, = 2 eV

= 2 × 1.6 × 10−19

= 3.2 × 10−19 J

Number of layers of sodium that absorbs theincident energy, n = 5

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

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

The incident power isuniformly absorbed by all the electrons continuously. Hence, the amount ofenergy absorbed per second per electron is:

Time required forphotoelectric emission:

Thetime required for the photoelectric emission is nearly half a year, which isnot practical. Hence, the wave picture is in disagreement with the givenexperiment.

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