A faint ultraviolet lamp gives an intensity of 2.0 × 10⁻³ W/m² on a metal plate with a work…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A faint ultraviolet lamp gives an intensity of on a metal plate with a work function of eV. Suppose light is a smooth wave, and one atom collects the light that falls on an area of . (a) How much power does one atom take in? (b) How long would one electron need to collect the work function? (c) The measured delay is less than s. By what factor is the time from the wave picture too long?
Need a reminder? The key ideaShow
In a photocell the saturation current is in proportion to the intensity. The largest kinetic energy of the electrons is , and it depends on the frequency, not on the intensity. There is no emission below the threshold frequency, and no delay above it.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Find the power one atom takes in. Then divide the work function, in joule, by that power.
Step 1. The power. .
Step 2. The energy. .
Step 3. The time. . That is about eleven minutes.
Step 4. The factor. .
Answer: W; s; a factor of .
Check. The wave picture says minutes, and the experiment says less than a billionth of a second. A photon gives its energy to one electron at once, and the delay disappears.
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