Beam Photoelectric
2009

Photoelectric Effect Einstein Question?
According to Einstein, increasing the brightness of a beam of light without changing its color will increase:
a) the energy of each photon
b) the speed of the photons
c) the frequency of the photons
d) the number of photons
e) none of the above
Einstein’s equation governing the photoelectric effect is the following:
E = hν – φ
where h is Planck’s constant, ν is the frequency of light incident on a metal, and E is the energy of the emitted electrons. The constant φ is called the metal’s “work function,” and the following equation correlates it to a threshold frequency below which no light, regardless of its intensity, will eject photoelectrons:
φ = (h)(ν_crit)
where h is again Planck’s constant, and ν_crit is the critical frequency.
Scientists had observed that when light was shone onto a metal, it often caused electrons to be ejected. However, while classical theories predicted that as the intensity of light increased, so should the energy of the emitted electrons, this was not observed. Instead, the energy was proportional to the frequency of the incident light, and moreover, light of too low a frequency (below the metal’s work function divided by Planck’s constant) did not cause any electrons to be emitted, not even at tremendous intensity.
Einstein’s equation demonstrates that light is quantized, and that the photoelectric effect involves the absorption of a light quanta. Recalling that the energy of light is directly related to its frequency, he reasoned that only light above some threshold energy (frequency) was sufficient to dislodge electrons from the metal. Furthermore, increasing the intensity of the light has no effect on the energy of the ejected electrons; their energy depends only on the energy (frequency) of the incident light.
So to answer your question, increasing the brightness of a beam of light incident on a metal without changing its color (frequency or energy) will not have any effect on the speed, energy, or frequency of either the incident photons, or the electrons emitted. Instead, since light is quantized, a brighter light simply means more photons, which are capable of ejecting more electrons. Hence, the answer is (d).
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