Physics: Photoelectric Effect and Wave-Particle Duality Worksheet

Question 1

A beam of green light has a wavelength of 500 nm. Calculate the energy of one photon in joules and in electron volts.

Accepted Answer

The photon energy is E = hc/lambda = (6.63 x 10^-34 J s)(3.00 x 10^8 m/s)/(500 x 10^-9 m) = 3.98 x 10^-19 J. In electron volts, this is (3.98 x 10^-19 J)/(1.60 x 10^-19 J/eV) = 2.49 eV.

Question 2

A metal has a threshold frequency of 5.00 x 10^14 Hz. Calculate its work function in joules and in electron volts.

Accepted Answer

The work function is the photon energy at the threshold frequency. It is W = hf = (6.63 x 10^-34 J s)(5.00 x 10^14 Hz) = 3.32 x 10^-19 J, which is 2.07 eV.

Question 3

Light with a wavelength of 400 nm shines on a metal with a work function of 2.0 eV. Determine whether electrons are emitted, and find the maximum kinetic energy of the emitted electrons.

Accepted Answer

The photon energy is E = 1240 eV nm / 400 nm = 3.10 eV. Since 3.10 eV is greater than the 2.0 eV work function, electrons are emitted. Their maximum kinetic energy is 3.10 eV - 2.0 eV = 1.10 eV.

Question 4

A metal is illuminated by light with a frequency above its threshold frequency. The intensity of the light is doubled while the frequency stays the same. Explain what happens to the number of emitted electrons and to their maximum kinetic energy.

Accepted Answer

Doubling the intensity increases the number of photons hitting the metal each second, so more electrons can be emitted. The maximum kinetic energy of the electrons does not change because it depends on the photon frequency, not on the intensity.

Question 5

Bright red light does not eject electrons from a metal surface, but dim violet light does. Explain why this supports the photon model of light.

Accepted Answer

This supports the photon model because electron emission depends on the energy of each photon. Violet light has a higher frequency and higher photon energy than red light, so even dim violet light can exceed the metal's threshold energy while bright red light cannot.

Question 6

Photoelectrons from a metal have a maximum kinetic energy of 0.85 eV. What stopping potential is needed to stop the most energetic electrons?

Accepted Answer

A stopping potential of 0.85 V is needed. Since 1 electron volt is the energy gained or lost by one electron moving through 1 volt, a maximum kinetic energy of 0.85 eV corresponds to a stopping voltage of 0.85 V.

Question 7

A graph of maximum kinetic energy of photoelectrons versus light frequency is a straight line. State what the slope and the x-intercept represent.

Accepted Answer

The slope of the graph represents Planck's constant, h. The x-intercept represents the threshold frequency, which is the minimum frequency needed for electrons to be emitted from the metal.

Question 8

An electron with mass 9.11 x 10^-31 kg moves at 2.00 x 10^6 m/s. Calculate its de Broglie wavelength.

Accepted Answer

The de Broglie wavelength is lambda = h/p = h/(mv). Substituting gives lambda = (6.63 x 10^-34 J s)/((9.11 x 10^-31 kg)(2.00 x 10^6 m/s)) = 3.64 x 10^-10 m.

Question 9

A 0.145 kg baseball travels at 40.0 m/s. Calculate its de Broglie wavelength and explain why its wave behavior is not noticeable in everyday life.

Accepted Answer

The baseball's wavelength is lambda = h/(mv) = (6.63 x 10^-34 J s)/((0.145 kg)(40.0 m/s)) = 1.14 x 10^-34 m. This wavelength is far too small to observe, so the baseball behaves like an ordinary classical object in everyday situations.

Question 10

Which has greater photon energy: a microwave photon with frequency 1.00 x 10^10 Hz or a visible light photon with frequency 6.00 x 10^14 Hz? Explain your answer.

Accepted Answer

The visible light photon has greater energy because photon energy is directly proportional to frequency. Since 6.00 x 10^14 Hz is much larger than 1.00 x 10^10 Hz, the visible photon has much more energy.

Question 11

In a double-slit experiment, very dim light is sent through the slits so that photons arrive one at a time. Over time, an interference pattern appears on the screen. Explain how this shows wave-particle duality.

Accepted Answer

Each photon is detected as a localized particle-like hit on the screen, but the overall pattern forms an interference pattern that is characteristic of waves. This shows that light has both particle-like and wave-like behavior.

Question 12

Classical wave theory predicted that a very bright low-frequency light beam should eventually eject electrons from a metal. In the photoelectric effect, this does not happen if the frequency is below the threshold frequency. Explain why.

Accepted Answer

Electrons absorb energy from individual photons. If each photon has less energy than the metal's work function, no electron can escape, no matter how bright the light is. Increasing brightness adds more low-energy photons, but it does not increase the energy of each photon.

Physics: Photoelectric Effect and Wave-Particle Duality

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