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Chapter 36: Problem 30

You illuminate a zinc surface with 550 -nm light. How high do you have to turn up the stopping voltage to squelch the photoelectric current completely?

Short Answer

Expert verified
Answer: The stopping voltage required to completely stop the photoelectric current is 0 volts.

Step by step solution

01

Identify the known values and required value

We are given the following information: - Wavelength of the light (\(\lambda\)) = 550 nm - Work function of zinc (\(\phi\)) = 4.3 eV (This value can be found in reference tables) We are asked to find the stopping voltage (\(V_s\)).
02

Convert wavelength to frequency

To convert the wavelength of the light to its frequency (\(f\)), we can use the following equation: \(f = \frac{c}{\lambda}\) Where \(c\) is the speed of light (\(3.00 \times 10^8 \, m/s\)) and \(\lambda\) is the wavelength of the light. Note that we need to convert the wavelength to meters: \(\lambda = 550 \, nm = 550 \times 10^{-9} \, m\) Now, we can calculate the frequency, \(f\): \(f = \frac{3.00 \times 10^8 \, m/s}{550 \times 10^{-9} \, m} = 5.45 \times 10^{14} \, Hz\)
03

Calculate the energy of the incident photons

Now we can calculate the energy of the incident photons (\(E\)) using the Planck's equation: \(E = h \times f\) Where \(h\) is the Planck's constant (\(6.63 \times 10^{-34} \, Js\)) and \(f\) is the frequency of the light. Now we can calculate \(E\): \(E = (6.63 \times 10^{-34} \, Js)(5.45 \times 10^{14} \, Hz) = 3.61 \times 10^{-19} \, J\) To make our calculations easier, we can convert this energy to electron volts (eV): \(E = 3.61 \times 10^{-19} \, J \times \frac{1 \, eV}{1.60 \times 10^{-19} \, J} = 2.26 \, eV\)
04

Calculate the maximum kinetic energy of the ejected electrons

The photoelectric effect equation relates the work function of zinc, the energy of the incident photons, and the maximum kinetic energy of the ejected electrons (\(K_{max}\)): \(K_{max} = E - \phi\) Now, we plug in the values for \(E\) and \(\phi\): \(K_{max} = 2.26 \, eV - 4.3 \, eV = -2.04 \, eV\) The negative value indicates that the energy of the incident photons is not sufficient to eject electrons from the zinc surface, hence no photoelectric current is generated.
05

Stopping voltage calculation

Since there is no photoelectric current, we do not need to apply any stopping voltage to squelch the photoelectric current. Therefore, the stopping voltage required is: \(V_s = 0\) So, the stopping voltage required to squelch the photoelectric current completely is 0 volts.

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Most popular questions from this chapter

The work function of a certain material is \(5.8 \mathrm{eV}\). What is the photoelectric threshold for this material?

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?

Consider a quantum state of energy \(E\), which can be occupied by any number \(n\) of some bosonic particles, including \(n=0\). At absolute temperature \(T\), the probability of finding \(n\) particles in the state is given by \(P_{n}=N \exp \left(-n E / k_{\mathrm{B}} T\right)\), where \(k_{\mathrm{B}}\) is Boltzmann's constant and the normalization factor \(N\) is determined by the requirement that all the probabilities sum to unity. Calculate the mean or expected value of \(n\), that is, the occupancy, of this state, given this probability distribution.

A nitrogen molecule of mass \(m=4.648 \cdot 10^{-26} \mathrm{~kg}\) has a speed of \(300.0 \mathrm{~m} /\mathrm{s}\).

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.
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