A photoelectric-effect experiment finds a stopping potential of 1.56 V when light of 200 nm is used to illuminate the cathode. From what metal is the cathode made?

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Determine the energy of the incident photons using the equation for photon energy: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J·s} \)), \( c \) is the speed of light (\( 3.00 \times 10^8 \, \text{m/s} \)), and \( \lambda \) is the wavelength of the light (200 nm, converted to meters as \( 200 \times 10^{-9} \)).

Convert the photon energy from joules to electron volts (eV) using the conversion factor \( 1 \text{ eV} = 1.602 \times 10^{-19} \, \text{J} \).

Relate the stopping potential \( V_s \) to the maximum kinetic energy of the ejected electrons using the equation \( K_{\text{max}} = eV_s \), where \( e \) is the elementary charge (\( 1.602 \times 10^{-19} \, \text{C} \)) and \( V_s = 1.56 \, \text{V} \).

Use the photoelectric equation \( E = \phi + K_{\text{max}} \), where \( \phi \) is the work function of the metal, \( E \) is the photon energy, and \( K_{\text{max}} \) is the maximum kinetic energy of the ejected electrons. Rearrange to solve for \( \phi \): \( \phi = E - K_{\text{max}} \).

Compare the calculated work function \( \phi \) (in eV) to known work functions of metals to identify the material of the cathode.

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주요 개념

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Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material (usually a metal) when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, as photons must have a minimum energy, known as the work function, to dislodge electrons from the material.

Stopping Potential

Stopping potential is the minimum voltage needed to stop the flow of photoelectrons emitted from a cathode in a photoelectric experiment. It is directly related to the kinetic energy of the emitted electrons, which can be calculated using the equation eV = KE, where e is the charge of the electron, V is the stopping potential, and KE is the kinetic energy of the electrons.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a metal. It is a characteristic property of each metal and is crucial in determining whether the energy of incoming photons (from light) is sufficient to overcome this barrier, thus allowing the photoelectric effect to occur.