The work function of silver metal is 436 kJ/mol. What frequency of light is needed to eject electrons from a sample of silver?

Verified step by step guidance

1. Identify the concept: The problem involves the photoelectric effect, where light of a certain frequency is needed to eject electrons from a metal surface.
2. Recall the formula for the energy of a photon: \( E = h \nu \), where \( E \) is the energy, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), and \( \nu \) is the frequency of the light.
3. Convert the work function from kJ/mol to J/photon. Since 1 mol contains Avogadro's number of particles \( (6.022 \times 10^{23} \text{ mol}^{-1}) \), divide the work function by Avogadro's number and convert kJ to J.
4. Set the energy of the photon equal to the work function: \( h \nu = \text{work function in J/photon} \).
5. Solve for the frequency \( \nu \) by rearranging the equation: \( \nu = \frac{\text{work function in J/photon}}{h} \).

Key Concepts

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material, typically measured in joules or kilojoules per mole. For silver, this value is given as 436 kJ/mol, indicating the energy needed to overcome the attractive forces holding the electrons in the metal.

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, where photons must have energy equal to or greater than the work function to eject electrons from the material.

Frequency and Energy Relationship

The energy of a photon is directly related to its frequency through the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the light. To find the frequency needed to eject electrons from silver, one must convert the work function from kJ/mol to joules per photon and then use this relationship.