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Chapter 36: Problem 29

In a photoelectric effect experiment, a laser beam of unknown wavelength is shined on a cesium cathode (work function \(\phi=2.100 \mathrm{eV}\) ). It is found that a stopping potential of \(0.310 \mathrm{~V}\) is needed to eliminate the current. Next, the same laser is shined on a cathode made of an unknown material, and a stopping potential of \(0.110 \mathrm{~V}\) is found to be needed to eliminate the current. a) What is the work function for the unknown cathode? b) What would be a possible candidate for the material of this unknown cathode?

Short Answer

Expert verified
Answer: The work function of the unknown cathode is approximately 1.90 eV. A possible candidate for the material of the unknown cathode is potassium (K), which has a work function of approximately 1.92 eV.

Step by step solution

01

Find the frequency of the light

First, use the equation for the stopping potential and work function to find the frequency of the light: \(0.310V = \frac{(h \times f) - (2.1eV)}{e}\) Solving for \(f\): \(f = \frac{0.310e + 2.1e}{h} = \frac{2.41e}{6.626 \times 10^{-34} \mathrm{Js}} \approx 3.63 \times 10^{15}\,\mathrm{Hz}\)
02

Find the work function of the unknown cathode

Now that we have the frequency of the light, we can use the stopping potential for the unknown material to find its work function: \(0.110 \mathrm{V} = \frac{(h \times f) - \phi_\mathrm{unknown}}{e}\) Solving for \(\phi_\mathrm{unknown}\): \(\phi_\mathrm{unknown} = (h \times f) - (0.110e) \approx 1.90\,\mathrm{eV}\) So, the work function for the unknown cathode is approximately \(1.90\,\mathrm{eV}\).
03

Suggest a possible candidate for the material of the unknown cathode

Based on the work function value, a possible candidate for the material of the unknown cathode is potassium (K), which has a work function of approximately \(1.92\,\mathrm{eV}\). Keep in mind, there are other materials with similar work functions, but potassium is one possible option given its close proximity to the calculated work function value.

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Most popular questions from this chapter

How many photons per second must strike a surface of area \(10.0 \mathrm{~m}^{2}\) to produce a force of \(0.100 \mathrm{~N}\) on the surface, if the photons are monochromatic light of wavelength \(600 . \mathrm{nm}\) ? Assume the photons are absorbed.

Alpha particles are accelerated through a potential difference of \(20.0 \mathrm{kV}\). What is their de Broglie wavelength?

A 50.0 -kg particle has a de Broglie wavelength of \(20.0 \mathrm{~cm} .\) a) How fast is the particle moving? b) What is the smallest speed uncertainty of the particle if its position uncertainty is \(20.0 \mathrm{~cm} ?\)

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Suppose that Fuzzy, a quantum-mechanical duck, lives in a world in which Planck's constant \(\hbar=1.00 \mathrm{~J}\) s. Fuzzy has a mass of \(0.500 \mathrm{~kg}\) and initially is known to be within a \(0.750-\mathrm{m}-\) wide pond. What is the minimum uncertainty in Fuzzy's speed? Assuming that this uncertainty prevails for \(5.00 \mathrm{~s}\), how far away could Fuzzy be from the pond after 5.00 s?
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