The photoelectric threshold wavelength of a tungsten surface is 272 nm. Calculate the maximum kinetic energy of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency 1.45 * 10^15 Hz. Express the answer in electron volts.

Verified step by step guidance

1. First, calculate the energy of the incident ultraviolet radiation using the formula $E = h \nu$, where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J s) and $\nu$ is the frequency of the radiation.
2. Next, determine the energy corresponding to the threshold wavelength using the formula $E_{\text{threshold}} = \frac{hc}{\lambda}$, where $c$ is the speed of light ($3.00 \times 10^8$ m/s) and $\lambda$ is the threshold wavelength.
3. Convert the threshold wavelength from nanometers to meters by multiplying by $10^{-9}$.
4. Calculate the maximum kinetic energy of the ejected electrons using the formula $K_{\text{max}} = E - E_{\text{threshold}}$, where $E$ is the energy of the incident radiation and $E_{\text{threshold}}$ is the energy at the threshold wavelength.
5. Convert the maximum kinetic energy from joules to electron volts by using the conversion factor $1 \text{ eV} = 1.602 \times 10^{-19}$ joules.

Key Concepts

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material when it absorbs light or electromagnetic radiation. This effect demonstrates the particle nature of light, where photons transfer energy to electrons. The energy of the incoming photons must exceed a certain threshold to liberate electrons, which is defined by the material's work function.

Threshold Wavelength

The threshold wavelength is the maximum wavelength of light that can cause the photoelectric effect in a given material. It is inversely related to the energy of the photons; shorter wavelengths correspond to higher energy. For tungsten, the threshold wavelength of 272 nm indicates that photons with wavelengths longer than this will not have enough energy to eject electrons.

Kinetic Energy of Ejected Electrons

The kinetic energy of ejected electrons in the photoelectric effect can be calculated using the equation KE = hf - φ, where KE is the kinetic energy, h is Planck's constant, f is the frequency of the incident light, and φ is the work function of the material. The work function can be derived from the threshold wavelength, allowing for the calculation of the maximum kinetic energy of the electrons when exposed to light of a specific frequency.