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.
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4.1.1) The photoelectric effect indicates the particle nature of light. This means that light energy comes in separate, individual packets (like tiny, distinct bundles) called photons, rather than a continuous stream. 4.1.2) The maximum speed of the ejected electrons will REMAIN THE SAME. Reason: The maximum kinetic energy (and thus maximum speed) of the ejected electrons depends on the frequency (or wavelength) of the incident light and the work function of the metal, not its intensity. Increasing the intensity of light only increases the number of photons, which in turn increases the number of ejected electrons, but not the energy of individual photons or the maximum kinetic energy of each electron. 4.1.3) Step 1: Convert the wavelength of incident light from nanometers to meters. = 420 nm = 420 × 10^-9 m Step 2: Calculate the energy of the incident photons using the formula E = (hc)/(). E = (6.63 × 10^-34 J·s)(3.0 × 10^8 m·s^-1)420 × 10^-9 m E = 1.989 × 10^-25 J·m420 × 10^-9 m E = 4.7357 × 10^-19 J Step 3: Calculate the maximum kinetic energy of the ejected electrons using the formula KE_max = (1)/(2)m_e v_max^2. KE_max = (1)/(2)(9.11 × 10^-31 kg)(4.76 × 10^5 m·s^-1)^2 KE_max = (1)/(2)(9.11 × 10^-31 kg)(2.26576 × 10^11 m^2·s^-2) KE_max = 1.0308 × 10^-19 J Step 4: Use the photoelectric equation E = W_0 + KE_max to find the work function (W_0) of the metal. W_0 = E - KE_max W_0 = (4.7357 × 10^-19 J) - (1.0308 × 10^-19 J) W_0 = 3.7049 × 10^-19 J Step 5: Calculate the threshold wavelength (_0) using the work function W_0 = (hc)/(_0). _0 = (hc)/(W_0) _0 = (6.63 × 10^-34 J·s)(3.0 × 10^8 m·s^-1)3.7049 × 10^-19 J _0 = 1.989 × 10^-25 J·m3.7049 × 10^-19 J _0 = 5.368 × 10^-7 m Step 6: Compare the calculated threshold wavelength with the values in the table. The calculated threshold wavelength (5.368 × 10^-7 m) is approximately equal to the threshold wavelength for Sodium (5.37 × 10^-7 m). The metal used in the experiment is Sodium. 4.2) The lines that correctly show transitions that will result in the atom giving off an EMISSION SPECTRUM are Q and S. Reason: An emission spectrum is produced when an electron transitions from a higher energy level to a lower energy level, releasing a photon of specific energy. Both Q (E2 to E1) and S (E3 to E1) represent such transitions. Got more? Send 'em!