The work function of a material is examined using the...

The work function of a material is examined using the apparatus shown schematically in Fig. $\mathbf{P} 38.38$. The ammeter measures the photocurrent. The voltage of the anode relative to the cathode is $V_{\mathrm{AC}}$. (a) The switch is in position $a$ while radiation with wavelength $140 \mathrm{nm}$ is incident on the cathode. The potentiometer is set at $R=3.20 \mathrm{k} \Omega$, and there is no photocurrent. What is the potential difference $V_{\mathrm{AC}} ?(\mathrm{~b})$ The resistance $R$ is slowly adjusted to lower values until the first hint of a photocurrent is detected in the ammeter. That happens when $R=334 \Omega$. What is the value of $V_{\mathrm{AC}}$ at that point? (c) What is the work function $\phi$ of the cathode material? (d) The switch is then thrown to position $b$ and the ammeter measures a photocurrent $i=3.71 \mathrm{~mA}$. What is the current $I$ in this case? (e) What is the value of $V_{\mathrm{AC}}$ ? (f) The switch is retumed to position $a$, and the wavelength of the light is reduced to $65.0 \mathrm{nm}$. The photocurrent increases. What is the minimum value of $R$ for which the photocurrent will cease?

The work function of a material is examined using the apparatus shown schematically in Fig. $\mathbf{P} 38.38$. The ammeter measures the photocurrent. The voltage of the anode relative to the cathode is $V_{\mathrm{AC}}$.
(a) The switch is in position $a$ while radiation with wavelength $140 \mathrm{nm}$ is incident on the cathode. The potentiometer is set at $R=3.20 \mathrm{k} \Omega$, and there is no photocurrent. What is the potential difference $V_{\mathrm{AC}} ?(\mathrm{~b})$ The resistance $R$ is slowly adjusted to lower values until the first hint of a photocurrent is detected in the ammeter. That happens when $R=334 \Omega$. What is the value of $V_{\mathrm{AC}}$ at that point? (c) What is the work function $\phi$ of the cathode material? (d) The switch is then thrown to position $b$ and the ammeter measures a photocurrent $i=3.71 \mathrm{~mA}$. What is the current $I$ in this case? (e) What is the value of $V_{\mathrm{AC}}$ ? (f) The switch is retumed to position $a$, and the wavelength of the light is reduced to $65.0 \mathrm{nm}$. The photocurrent increases. What is the minimum value of $R$ for which the photocurrent will cease?

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Key Concepts

Photoelectric Effect

This is the phenomenon in which electrons are emitted from a material's surface as a result of exposure to light of sufficient frequency. It was key in establishing quantum theory and demonstrates that light can behave as both a wave and a particle.

Work Function

This is the minimum energy required to remove an electron from the surface of a material. It is a fundamental property of the material and determines the threshold frequency of light needed to initiate electron emission.

Stopping Potential

Also known as the cutoff potential, it is the minimum voltage required to stop the most energetic emitted electrons, effectively reducing the photocurrent to zero. It provides a direct measurement of the maximum kinetic energy of the photoelectrons.

Photon Energy

This concept involves the energy a photon carries, calculated by the formula E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the radiation. The photon energy must exceed the work function for electron emission to occur.

Photocurrent Measurement

Photocurrent refers to the electrical current generated by the photoemission of electrons. Its measurement in different circuit configurations allows the investigation of electron kinetic energies and the properties of the material's surface under illumination.

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