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Chapter 27: Problem 9

Ultraviolet light of wavelength 220 nm illuminates a tungsten surface and electrons are ejected. A stopping potential of \(1.1 \mathrm{V}\) is able to just prevent any of the ejected electrons from reaching the opposite electrode. What is the work function for tungsten?

Short Answer

Expert verified
Answer: The work function of tungsten is \(7.27 * 10^{-19}\) Joules.

Step by step solution

01

Identify and list given informations

We have the following informations: - Wavelength of ultraviolet light (λ): 220 nm - Stopping potential (V_stop): 1.1 V
02

Understand the photoelectric effect equation

The photoelectric effect equation is given by: \(E = W + K_{max}\) where: - E is the energy of the incident light - W is the work function - \(K_{max}\) is the maximum kinetic energy of the ejected electrons The goal is to find the work function (W) for tungsten.
03

Calculate the energy of the incident light

First, let's convert the wavelength of ultraviolet light λ from nanometers to meters: λ = 220 nm * 10^{-9} m/nm = 2.20 * 10^{-7} m Then, use the equation for energy (E) based on the speed of light (c), Planck's constant (h), and the wavelength (λ): \(E = \dfrac{hc}{λ}\) Substitute the values of h = 6.63 * 10^{-34} J*s and c = 3.00 * 10^8 m/s: \(E = \dfrac{(6.63 * 10^{-34} \text{J*s})(3.00 * 10^8 \text{m/s})}{(2.20 * 10^{-7} \text{m})}\) \(E = 9.03 * 10^{-19}\) J
04

Calculate the maximum kinetic energy of the ejected electrons

Using the stopping potential (V_stop) and the charge of an electron (e = 1.60 * 10^{-19} C), find the maximum kinetic energy (K_max): \(K_{max} = e * V_{stop}\) \(K_{max} = (1.60 * 10^{-19} \text{C}) * (1.1 \text{V})\) \(K_{max} = 1.76 * 10^{-19}\) J
05

Calculate the work function

Now, use the photoelectric effect equation to find the work function (W): \(E = W + K_{max}\) Isolate the work function (W): \(W = E - K_{max}\) Substitute the values of E and K_max found in Steps 3 and 4: \(W = (9.03 * 10^{-19} \text{J}) - (1.76 * 10^{-19} \text{J})\) \(W = 7.27 * 10^{-19}\) J The work function for tungsten is \(7.27 * 10^{-19}\) Joules.

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