Which type of electromagnetic radiation will cause the greatest number of electrons to be ejected from zinc metal with a work function of 350 kJ/mol? (LO 5.4, 5.5) (a) Dim light with a wavelength of 320 nm (b) Dim light with a wavelength of 360 nm (c) Bright light with a wavelength of 360 nm (d) Bright light with a wavelength of 375 nm

Verified step by step guidance

1. Convert the work function from kJ/mol to Joules per electron by using Avogadro's number. The work function in Joules per electron is calculated by dividing the given work function by Avogadro's number (approximately 6.022 \(\times\) 10^23 mol^-1).
2. Calculate the energy of the photons for each wavelength using the equation \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant (6.626 \(\times\) 10^-34 J s), \(c\) is the speed of light (3.00 \(\times\) 10^8 m/s), and \(\lambda\) is the wavelength in meters.
3. Convert the wavelengths from nanometers to meters by multiplying by 10^-9.
4. Compare the photon energy calculated for each wavelength to the work function energy in Joules per electron. Only photons with energy equal to or greater than the work function can eject electrons.
5. Identify which option(s) have photon energies that meet or exceed the work function energy. The intensity (brightness) of the light does not affect the energy per photon, so it does not influence which type of light ejects more electrons, but rather how many electrons are ejected if the energy condition is met.

Key Concepts

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material when it absorbs light or electromagnetic radiation. The energy of the incoming photons must exceed the work function of the material for electrons to be ejected. This concept is crucial for understanding how light interacts with metals and the conditions necessary for electron emission.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is typically expressed in electron volts (eV) or kilojoules per mole (kJ/mol). In this question, zinc has a work function of 350 kJ/mol, meaning that only photons with energy greater than this value can cause electron ejection.

Photon Energy and Wavelength

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Shorter wavelengths correspond to higher energy photons. Understanding this relationship is essential for determining which light sources can effectively eject electrons from zinc.