This question tests understanding of atomic line spectra and quantized energy levels. Line spectra demonstrate that electrons in atoms can only occupy specific, discrete energy levels, a fundamental principle of quantum mechanics. When electrons transition between these quantized levels, they emit photons with energies exactly equal to the energy difference between levels. Since energy levels are fixed for a given element, the emitted photon energies (and thus wavelengths via E = hc/λ) are also discrete and characteristic. The three observed wavelengths correspond to specific electronic transitions in hydrogen atoms. This contrasts with continuous spectra from hot solids, where thermal motion produces a broad range of energies. The discrete nature of the spectrum provides direct evidence for quantization in atomic systems, distinguishing it from classical predictions of continuous emission.

This question tests understanding of how photon frequency affects the photoelectric effect. The photoelectric effect demonstrates that the maximum kinetic energy of emitted electrons depends directly on photon frequency through the relationship KEmax = hf - φ. When frequency doubles from f to 2f, the photon energy doubles from hf to 2hf. Since the work function φ remains constant for the same metal, the maximum kinetic energy increases by hf. The stopping potential, which measures this maximum kinetic energy through eVs = KEmax, must therefore increase. This linear relationship between frequency and stopping potential is a key prediction of the photon model. Common misconceptions include thinking that frequency affects the number of electrons rather than their energy, or that intensity determines electron energy.

This question tests understanding of how light intensity affects the photoelectric effect when frequency is held constant. The photoelectric effect demonstrates that electron emission depends on individual photon energy (determined by frequency), not the total light intensity. When intensity increases at constant frequency, more photons strike the surface per unit time, but each photon still has the same energy. Since the stopping potential depends only on the maximum kinetic energy of emitted electrons (which equals photon energy minus work function), it remains unchanged. However, more photons mean more electrons are emitted, increasing the photocurrent. The common misconception is that higher intensity means more energy per electron, but in the quantum model, each electron absorbs exactly one photon regardless of intensity.

This question tests the fundamental principle of the photoelectric effect regarding threshold frequency. The photoelectric effect reveals that electron emission requires individual photons to have sufficient energy to overcome the material's work function, demonstrating energy quantization. At frequency f₁, no emission occurs because photon energy (hf₁) is less than the work function, regardless of intensity. At f₂, photon energy exceeds the work function, enabling electron emission. This observation directly contradicts classical wave theory, which would predict that sufficient intensity at any frequency could provide enough total energy for emission. The key insight is that energy transfer occurs in discrete quanta (photons), and each electron-photon interaction is independent. Common distractors incorrectly suggest that intensity alone determines emission or misunderstand the relationship between stopping potential and photon properties.

This question tests understanding of how photon frequency affects electron kinetic energy in the photoelectric effect. The photoelectric effect follows the energy conservation equation: hf = φ + KEmax, where the photon energy is divided between overcoming the work function and providing kinetic energy to the electron. When frequency decreases while remaining above threshold, the photon energy (hf) decreases. Since the work function φ is constant for a given metal, the maximum kinetic energy of emitted electrons must decrease. The stopping potential, related by eVs = KEmax, therefore decreases proportionally. Intensity affects only the number of photons (and thus electrons), not the energy per electron. This demonstrates the particle nature of light, where each photon's energy depends solely on its frequency, not the beam intensity.

This question tests understanding of how wavelength relates to photon energy in the photoelectric effect. The relationship E = hc/λ shows that photon energy is inversely proportional to wavelength - as wavelength decreases, photon energy increases. When wavelength shifts toward ultraviolet (shorter λ), frequency increases and photon energy rises. In the photoelectric effect, this increased photon energy translates directly to increased maximum kinetic energy of emitted electrons, following KEmax = hf - φ. Since the work function φ remains constant for the same metal, any increase in photon energy appears as increased electron kinetic energy. The stopping potential, which measures this maximum kinetic energy, therefore increases. Common misconceptions include thinking that wavelength affects the number of electrons or that ultraviolet light cannot cause emission.

This question tests understanding of the linear relationship between stopping potential and frequency in the photoelectric effect. The photoelectric equation eVs = hf - φ predicts that stopping potential varies linearly with frequency, with slope h/e. This relationship arises because each photon's energy (hf) is divided between overcoming the work function (φ) and providing kinetic energy to the electron (eVs). The positive slope indicates that higher frequency photons impart more kinetic energy to electrons after overcoming the constant work function. This linear relationship was crucial historical evidence for the photon model of light, as it directly contradicts classical wave predictions. The slope's value provides a method to measure Planck's constant, while the x-intercept gives the threshold frequency. Common misconceptions involve confusing the roles of frequency and intensity in determining electron energy.

This question tests understanding of the linear relationship between stopping potential and frequency. The photoelectric equation eVs = hf - φ can be rearranged to show Vs = (h/e)f - φ/e, revealing a linear relationship with slope h/e. When frequency increases by Δf, the stopping potential increases by ΔVs = (h/e)Δf. The 0.20 V increase for a frequency increase of Δf confirms this linear relationship. This linearity is a fundamental prediction of the photon model and was historically important in validating quantum theory. The relationship shows that each unit increase in frequency produces the same increase in stopping potential, regardless of the starting frequency. This constant slope h/e provides a method to measure Planck's constant and demonstrates that photon energy depends linearly on frequency.

This question tests understanding of the threshold frequency concept in the photoelectric effect. The photoelectric effect demonstrates that electron emission requires individual photons to have energy exceeding the work function, regardless of total light intensity. When frequency is below threshold, each photon has energy less than the work function (hf < φ), making electron emission impossible. Increasing intensity only increases the number of these insufficient-energy photons, not their individual energies. This observation was crucial evidence against classical wave theory, which predicted that sufficient intensity at any frequency could accumulate enough energy for emission. The quantum nature of light means energy transfer occurs in discrete packets, and each electron-photon interaction is independent. No amount of low-energy photons can combine to eject a single electron.

This question tests understanding of how discharge tube conditions affect emission spectra. Line spectra wavelengths are determined by the quantized energy differences between atomic levels, which are intrinsic properties of the atom and do not change with external conditions like tube voltage. Higher accelerating voltage increases the kinetic energy of electrons colliding with gas atoms, leading to more frequent excitations and more atoms in excited states per unit time. This increases the number of photons emitted (brightness) without changing their energies or wavelengths. The observation that wavelengths remain constant while intensity increases confirms that atomic energy levels are fixed properties. This principle underlies spectroscopic identification of elements, as emission wavelengths serve as unique fingerprints regardless of excitation conditions.