Light of different frequencies is incident on a metal plate. The sketch graph below shows the relationship between the maximum kinetic energy, Ekm, of the photoelectrons and the energy of the incident photons.

Question

Asked on August 6, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-08-06T04:39:27.018Z

10.1 The work function of a metal is the minimum energy required to eject an electron from the surface of the metal. 10.2 Step 1: The photoelectric effect equation is given by E_photon = W_0 + E_k,max, where E_photon is the energy of the incident photon, W_0 is the work function, and E_k,max is the maximum kinetic energy of the emitted photoelectron. Step 2: Rearranging the equation to match the graph's axes (E_k,max on y-axis, E_photon on x-axis): E_k,max = E_photon - W_0 This equation is in the form y = mx + c, where m is the gradient. Step 3: Comparing the equation to the graph, the gradient m is the coefficient of E_photon, which is 1. The numerical value of the gradient is 1. 10.3 10.3.1 Step 1: From the graph, when the energy of photons is Y, the maximum kinetic energy of the photoelectrons (E_k,max) is 2.99 × 10^-19 J. Step 2: Use the formula for maximum kinetic energy: E_k,max = (1)/(2)mv^2. The mass of an electron (m_e) is 9.11 × 10^-31 kg. 2.99 × 10^-19 J = (1)/(2) (9.11 × 10^-31 kg) v^2 Step 3: Solve for v^2: v^2 = 2 × 2.99 × 10^-19 J9.11 × 10^-31 kg v^2 = 5.98 × 10^-199.11 × 10^-31 m^2/s^2 v^2 ≈ 6.564 × 10^11 m^2/s^2 Step 4: Calculate v: v = sqrt(6.564 × 10^11) m^2/s^2 v ≈ 8.10 × 10^5 m/s 10.3.2 Step 1: From the graph, the x-intercept represents the work function (W_0), which is the minimum energy required to eject an electron (where E_k,max = 0). W_0 = 3.66 × 10^-19 J Step 2: At point Y, the maximum kinetic energy (E_k,max) is 2.99 × 10^-19 J. Use the photoelectric equation: E_photon = W_0 + E_k,max. Y = 3.66 × 10^-19 J + 2.99 × 10^-19 J Step 3: Calculate the value of Y: Y = (3.66 + 2.99) × 10^-19 J Y = 6.65 × 10^-19 J 10.4 The maximum kinetic energy of the photoelectrons will REMAIN THE SAME. Reason: The maximum kinetic energy of photoelectrons depends only on the energy (or frequency) of the individual incident photons and the work function of the metal. It does not depend on the intensity (number of photons per second) of the incident light. Increasing the number of photons per second only increases the number of photoelectrons emitted, not their individual maximum kinetic energy. Send me the next one 📸

Accepted Answer · 2026-08-06T04:39:27.018Z

10.1 The work function of a metal is the minimum energy required to eject an electron from the surface of the metal. 10.2 Step 1: The photoelectric effect equation is given by E_photon = W_0 + E_k,max, where E_photon is the energy of the incident photon, W_0 is the work function, and E_k,max is the maximum kinetic energy of the emitted photoelectron. Step 2: Rearranging the equation to match the graph's axes (E_k,max on y-axis, E_photon on x-axis): E_k,max = E_photon - W_0 This equation is in the form y = mx + c, where m is the gradient. Step 3: Comparing the equation to the graph, the gradient m is the coefficient of E_photon, which is 1. The numerical value of the gradient is 1. 10.3 10.3.1 Step 1: From the graph, when the energy of photons is Y, the maximum kinetic energy of the photoelectrons (E_k,max) is 2.99 × 10^-19 J. Step 2: Use the formula for maximum kinetic energy: E_k,max = (1)/(2)mv^2. The mass of an electron (m_e) is 9.11 × 10^-31 kg. 2.99 × 10^-19 J = (1)/(2) (9.11 × 10^-31 kg) v^2 Step 3: Solve for v^2: v^2 = 2 × 2.99 × 10^-19 J9.11 × 10^-31 kg v^2 = 5.98 × 10^-199.11 × 10^-31 m^2/s^2 v^2 ≈ 6.564 × 10^11 m^2/s^2 Step 4: Calculate v: v = sqrt(6.564 × 10^11) m^2/s^2 v ≈ 8.10 × 10^5 m/s 10.3.2 Step 1: From the graph, the x-intercept represents the work function (W_0), which is the minimum energy required to eject an electron (where E_k,max = 0). W_0 = 3.66 × 10^-19 J Step 2: At point Y, the maximum kinetic energy (E_k,max) is 2.99 × 10^-19 J. Use the photoelectric equation: E_photon = W_0 + E_k,max. Y = 3.66 × 10^-19 J + 2.99 × 10^-19 J Step 3: Calculate the value of Y: Y = (3.66 + 2.99) × 10^-19 J Y = 6.65 × 10^-19 J 10.4 The maximum kinetic energy of the photoelectrons will REMAIN THE SAME. Reason: The maximum kinetic energy of photoelectrons depends only on the energy (or frequency) of the individual incident photons and the work function of the metal. It does not depend on the intensity (number of photons per second) of the incident light. Increasing the number of photons per second only increases the number of photoelectrons emitted, not their individual maximum kinetic energy. Send me the next one 📸

Light of different frequencies is incident on a metal plate. The sketch graph below shows the relationship between the maximum kinetic energy, Ekm, of the photoelectrons and the energy of the incident photons.

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Light of different frequencies is incident on a metal plate. The sketch graph below shows the relationship between the maximum kinetic energy, Ekm, of the photoelectrons and the energy of the incident photons.

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