5. One prediction of the classical explanation for the photoelectric effect this

Question

5. One prediction of the classical explanation for the photoelectric effect this that low intensity light will take longer to start ejecting electrons than high intensity light. Let's do a calculation to show this. In order to eject an electron, the average thermal energy of the electrons needs to be comparable to the metal's work function. Let's use ksT as the thermal energy of the electrons (ks is Boltzmann's constant), assume the metal starts at room temperature, and assume current beings when kBT = 0.1 Eo. a) Suppose you have a 1.0 Watt laser striking a 0.1 gram piece of copper. How long will it take before the metal starts ejecting electrons? (Hint: How did you calculate the energy required for a given temperature change in thermodynamics?) in this case? to cause electrons to be ejected. How do the results from the 0.5 Watt laser differ from b) Suppose instead you use a 0.5 Watt laser with the same wavelength. How long would it take e) Photoelectric effect experiments show that the 0.5 Watt laser does not actually take longer those of the 1.0 Watt laser?

Explanation / Answer

Given, K0T = 0.1 E0

We know that, Power (P) = Work (W)/Time (t) ------(1)

a). Given P= 1.0 Watt, W= 0.1 E0, Time t = ?

Sub. above values in Equ (1) => 1.0 Watt = 0.1 E0/ t

=> t   = 0.1 E0/1.0 Watt

=> t    = 0.1 E0   sec

    b). Given P= 0.5 Watt, W= 0.1 E0, Time t = ?

Sub. above values in Equ (1) => 0.5 Watt = 0.1 E0/ t

=> t   = 0.1 E0/0.5 Watt

=> t    = 0.2 E0 sec

(c) Difference is due to the fact that,rarely, an electron will escape by absorbing two or more quanta. However, this is extremely rare because by the time it absorbs enough quanta to escape, the electron will probably have emitted the rest of the quanta.

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