NCERT Class XII Chapter
Dual Nature of Radiation and Matter
Questions With Solutions

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Question : 30
Total: 37
Light of intensity 105Wm2 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 wavepicture of radiation. The work function for the metal is given to be about 2 eV. What is the implication of your answer?
Solution:  
Wave picture of radiation state that incident energy is uniformly distributed among all the electrons continuously. Let us first calculate the total number of recipient electrons in 5 layers of sodium.
Consider each sodium atom has one electron free as conduction electron.
Effective atomic area = 1020m2
Number of conduction electrons in 5 layers
n =
5×areaofeachlayer
effectiveareaofeachatom
or n =
5×2×104
1020
= 1017
Incident power = incident intensity × area = 105×2×104 = 2 × 109 W
As incident energy is equally distributed among all conduction electrons.
Energy to each conduction electron per second =
2×109
1017
= 2 × 1026 W
Time required for emission by each electron
t =
totalworkfunctionenergy
energyreceivedpersecond

t =
2eV
2×1026W
=
2×1.6×1019
2×1026
= 1.6 × 107 s = 0.5 year
where experimental observation shows that emission of photoelectrons is instantaneous ≈ 109 sec
Thus, wave picture fails to explain photoelectric effect.
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