Potassium and gold cathodes are used in a photoelectric-effect experiment. For each cathode, find: The threshold frequency.

Verified step by step guidance

1. Understand the concept: The photoelectric effect occurs when light of a certain frequency (or higher) strikes a material, causing electrons to be ejected. The threshold frequency \( f_{\text{threshold}} \) is the minimum frequency of light required to eject electrons from the material. It is related to the work function \( \phi \) of the material by the equation \( f_{\text{threshold}} = \frac{\phi}{h} \), where \( h \) is Planck's constant.
2. Identify the work function \( \phi \) for each material: Look up the work function values for potassium and gold. For potassium, \( \phi \approx 2.3 \; \text{eV} \), and for gold, \( \phi \approx 5.1 \; \text{eV} \).
3. Convert the work function \( \phi \) from electron volts (eV) to joules (J): Use the conversion factor \( 1 \; \text{eV} = 1.602 \times 10^{-19} \; \text{J} \). For potassium, \( \phi_{\text{K}} = 2.3 \times 1.602 \times 10^{-19} \; \text{J} \). For gold, \( \phi_{\text{Au}} = 5.1 \times 1.602 \times 10^{-19} \; \text{J} \).
4. Calculate the threshold frequency \( f_{\text{threshold}} \) for each material: Use the formula \( f_{\text{threshold}} = \frac{\phi}{h} \), where \( h = 6.626 \times 10^{-34} \; \text{J·s} \) is Planck's constant. Substitute the work function values in joules for potassium and gold into the equation.
5. Express the results: The threshold frequency \( f_{\text{threshold}} \) for potassium and gold will be in units of hertz (Hz). Ensure the calculations are consistent and verify the units throughout the process.

Key Concepts

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light or electromagnetic radiation. This effect demonstrates the particle nature of light, as photons must have sufficient energy to overcome the work function of the material, leading to electron emission. Understanding this concept is crucial for analyzing how different materials respond to light.

Threshold Frequency

The threshold frequency is the minimum frequency of incident light required to eject electrons from a material's surface in the photoelectric effect. It is directly related to the work function of the material, which is the energy needed to remove an electron. If the frequency of the incoming light is below this threshold, no electrons will be emitted, regardless of the light's intensity.

Work Function

The work function is a material-specific constant that represents the minimum energy needed to remove an electron from the surface of a material. It is typically expressed in electron volts (eV) and varies between different materials, such as potassium and gold. The work function is essential for calculating the threshold frequency, as it determines the energy required for the photoelectric effect to occur.