The photoelectric effect threshold wavelength for a certain...

The photoelectric effect threshold wavelength for a certain metal is $400 \mathrm{nm}$. Calculate the maximum speed of photoelectrons if we use light having a wavelength of
(a) $300 \mathrm{nm}$
(b) $400 \mathrm{nm},$ and
(c) $500 \mathrm{nm}$

Key Concepts

Non-relativistic Kinetic Energy Equation

For photoelectrons moving at speeds much lower than the speed of light, the classical kinetic energy formula K = ½ mv² is used to relate the electron's kinetic energy to its speed. This relationship is applied after calculating the kinetic energy from Einstein’s equation to determine the maximum speed of the photoelectrons.

Einstein's Photoelectric Equation

Einstein's photoelectric equation relates the energy of an incident photon to the work function of the material and the maximum kinetic energy of the ejected electron. The equation is given by E_photon = ? + K_max, where E_photon is the energy of the photon, ? is the work function, and K_max is the maximum kinetic energy of the emitted electrons. This equation is fundamental for analyzing and predicting the outcomes of photoelectric experiments.

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are ejected from a material when it is exposed to electromagnetic radiation of sufficiently high frequency. It was one of the key experiments that provided evidence for the quantization of light and led to the development of quantum mechanics.

Work Function and Threshold Wavelength

The work function is the minimum energy required to remove an electron from the surface of a metal. The threshold wavelength is directly related to this work function; it is the maximum wavelength (or minimum frequency) of light that can cause the photoelectric effect. Light with a longer wavelength than the threshold will not eject electrons because its photons do not carry enough energy.

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