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The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm. What is the maximum velocity of the electrons ejected, in km/s, when light of wavelength 150. nm shines on a copper plate? Answer= km/s

The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm. What is the maximum velocity of the electrons ejected, in km/s, when light of wavelength 150. nm shines on a copper plate? Answer= km/s

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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**Photoelectric Effect on Copper Plate** The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm. What is the maximum velocity of the electrons ejected, in km/s, when light of wavelength 150 nm shines on a copper plate? **Answer:** ____ km/s --- For further understanding, let's break down the given information and solve this step-by-step: 1. **Identify the Work Function (Φ):** - The threshold wavelength (λ₀) for ejecting electrons is given as 243 nm. - The energy corresponding to this wavelength (work function) can be calculated using \( E = \frac{hc}{λ₀} \), where: - \( E \) is the energy, - \( h \) is Planck's constant (~6.626 x 10⁻³⁴ Js), - \( c \) is the speed of light (~3 x 10⁸ m/s), and - \( λ₀ \) is the threshold wavelength. 2. **Calculate the Energy of Incoming Photon:** - The wavelength of the incident light is 150 nm. - The energy of this photon is calculated by \( E_{\text{photon}} = \frac{hc}{λ_{\text{incident}}} \). 3. **Determine Kinetic Energy (KE) of Ejected Electrons:** - The kinetic energy of the ejected electrons is given by \( KE = E_{\text{photon}} - Φ \). 4. **Calculate Velocity:** - The maximum velocity \( v \) of the ejected electrons can be found using the kinetic energy formula \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the electron (~9.109 x 10⁻³¹ kg). By following these steps, we can determine the theoretical maximum velocity of the electrons ejected from a copper plate when illuminated with light of a specific wavelength.
Transcribed Image Text:**Photoelectric Effect on Copper Plate** The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm. What is the maximum velocity of the electrons ejected, in km/s, when light of wavelength 150 nm shines on a copper plate? **Answer:** ____ km/s --- For further understanding, let's break down the given information and solve this step-by-step: 1. **Identify the Work Function (Φ):** - The threshold wavelength (λ₀) for ejecting electrons is given as 243 nm. - The energy corresponding to this wavelength (work function) can be calculated using \( E = \frac{hc}{λ₀} \), where: - \( E \) is the energy, - \( h \) is Planck's constant (~6.626 x 10⁻³⁴ Js), - \( c \) is the speed of light (~3 x 10⁸ m/s), and - \( λ₀ \) is the threshold wavelength. 2. **Calculate the Energy of Incoming Photon:** - The wavelength of the incident light is 150 nm. - The energy of this photon is calculated by \( E_{\text{photon}} = \frac{hc}{λ_{\text{incident}}} \). 3. **Determine Kinetic Energy (KE) of Ejected Electrons:** - The kinetic energy of the ejected electrons is given by \( KE = E_{\text{photon}} - Φ \). 4. **Calculate Velocity:** - The maximum velocity \( v \) of the ejected electrons can be found using the kinetic energy formula \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the electron (~9.109 x 10⁻³¹ kg). By following these steps, we can determine the theoretical maximum velocity of the electrons ejected from a copper plate when illuminated with light of a specific wavelength.
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