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Part 1: Calculate the quantum of energy for a radiation. Step 1: State the formula for the energy of a photon. The quantum energy E of radiation is given by Planck's relation: E = hf where h is Planck's constant and f is the frequency of the radiation. Step 2: Substitute the given values. We are given h = 6.63 × 10^-34 J s and f = 2.5 × 10^14 Hz. 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 energy of the radiation is 1.6575 × 10^-19 J. Part 2: Work function and photoelectric effect. a) Express the work function in Joules. Step 1: Convert the work function from eV to Joules. The work function W_0 is given as 3.0 eV. The conversion factor is 1 eV = 1.6 × 10^-19 J. W_0 = 3.0 eV × (1.6 × 10^-19 JeV) Step 2: Calculate the work function in Joules. W_0 = 4.8 × 10^-19 J The work function in Joules is 4.8 × 10^-19 J. b) Determine the maximum kinetic energy of the photoelectrons and the threshold frequency. Step 1: Convert the wavelength to meters and calculate the energy of the incident photon. The wavelength = 3.5 nm. We know that 1 nm = 10^-9 m. So, = 3.5 × 10^-9 m. Planck's constant h = 6.64 × 10^-34 J s (for this part). The speed of light c = 3.0 × 10^8 m/s. The energy of the incident photon E is given by: E = (hc)/() E = (6.64 × 10^-34 J s) × (3.0 × 10^8 m/s)3.5 × 10^-9 m Step 2: Calculate the energy of the incident photon. E = 19.92 × 10^-263.5 × 10^-9 J E ≈ 5.6914 × 10^-17 J Step 3: Calculate the maximum kinetic energy of the photoelectrons. The photoelectric effect equation is E = W_0 + K_max, where K_max is the maximum kinetic energy. Therefore, K_max = E - W_0. We have W_0 = 4.8 × 10^-19 J (calculated previously). K_max = (5.6914 × 10^-17 J) - (4.8 × 10^-19 J) To subtract, we need to have the same power of 10: K_max = (569.14 × 10^-19 J) - (4.8 × 10^-19 J) K_max = (569.14 - 4.8) × 10^-19 J K_max = 564.34 × 10^-19 J K_max = 5.6434 × 10^-17 J The maximum kinetic energy of the photoelectrons is 5.6434 × 10^-17 J. Step 4: Calculate the threshold frequency. The threshold frequency f_0 is the minimum frequency required to eject an electron, and it is related to the work function by W_0 = hf_0. Therefore, f_0 = (W_0)/(h). We use W_0 = 4.8 × 10^-19 J and h = 6.64 × 10^-34 J s. f_0 = 4.8 × 10^-19 J6.64 × 10^-34 J s Step 5: Calculate the threshold frequency. f_0 ≈ 0.72289 × 10^15 Hz f_0 ≈ 7.2289 × 10^14 Hz The threshold frequency is 7.2289 × 10^14 Hz. Envoie-moi la prochaine 📸