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Here are the solutions to your questions: 1. Calculate the quantum of energy for a radiation of frequency 2.5 × 10^14 Hz. Step 1: State the formula for the energy of a photon. The energy of a quantum of radiation (photon) is given by Planck's equation: E = h where E is the energy, h is Planck's constant, and is the frequency. Step 2: Substitute the given values into the formula. Given: = 2.5 × 10^14 Hz h = 6.63 × 10^-34 J s E = (6.63 × 10^-34 J s) × (2.5 × 10^14 Hz) Step 3: Calculate the energy. E = 16.575 × 10^-20 J E = 1.6575 × 10^-19 J The quantum of energy is 1.66 × 10^-19 J (rounded to three significant figures). 2. The work function of a metal is 3.0 eV. a) Express this energy in Joules. Step 1: Use the given conversion factor. Given: Work function () = 3.0 eV Conversion factor: 1 eV = 1.6 × 10^-19 J = 3.0 eV × 1.6 × 10^-19 J1 eV Step 2: Calculate the work function in Joules. = 4.8 × 10^-19 J The work function in Joules is 4.8 × 10^-19 J b) The metal surface is illuminated by electromagnetic radiation of wavelength 3.5 nanometers. Determine the maximum kinetic energy (KE) of the photoelectron. Step 1: Calculate the energy of the incident photon. The energy of an incident photon is given by E = (hc)/(). Given: Wavelength () = 3.5 nanometers = 3.5 × 10^-9 m Planck's constant (h) = 6.64 × 10^-34 J s (using the value provided in this part of the question) Speed of light (c) = 3.0 × 10^8 m/s (standard value) E = (6.64 × 10^-34 J s) × (3.0 × 10^8 m/s)3.5 × 10^-9 m E = 19.92 × 10^-263.5 × 10^-9 J E ≈ 5.6914 × 10^-17 J Step 2: Calculate the maximum kinetic energy using the photoelectric effect equation. The maximum kinetic energy (KE_max) of the photoelectron is given by: KE_max = E - KE_max = (5.6914 × 10^-17 J) - (4.8 × 10^-19 J) To subtract, ensure the exponents are the same: KE_max = (569.14 × 10^-19 J) - (4.8 × 10^-19 J) KE_max = 564.34 × 10^-19 J KE_max = 5.6434 × 10^-17 J The maximum kinetic energy is 5.64 × 10^-17 J (rounded to three significant figures). c) Determine the threshold frequency. Step 1: State the formula for threshold frequency. The threshold frequency (_0) is the minimum frequency of incident radiation required to cause photoemission, and it is related to the work function by: = h_0 _0 = ()/(h) Step 2: Substitute the work function (in Joules) and Planck's constant. Given: = 4.8 × 10^-19 J h = 6.64 × 10^-34 J s _0 = 4.8 × 10^-19 J6.64 × 10^-34 J s Step 3: Calculate the threshold frequency. _0 ≈ 0.72289 × 10^15 Hz _0 ≈ 7.23 × 10^14 Hz The threshold frequency is 7.23 × 10^14 Hz (rounded to three significant figures). That's 2 down. 3 left today — send the next one.