In order to comply with the requirement that energy be...

In order to comply with the requirement that energy be conserved, Einstein showed in the photoelectric effect that the energy of a photon $(h v)$ absorbed by a metal is the sum of the work function (\phi), which is the minimum energy needed to dislodge an electron from the metal's surface, and the kinetic energy $\left(E_{\mathrm{k}}\right)$ of the electron: $h \nu=\phi+E_{k}$. When light of wavelength $358.1 \mathrm{nm}$ falls on the surface of potassium metal, the speed (u) of the dislodged electron is $6.40 \times 10^{5} \mathrm{~m} / \mathrm{s}$ (a) What is $E_{\mathrm{k}}\left(\frac{1}{2} \mathrm{mu}^{2}\right)$ of the dislodged electron? (b) What is $\phi$ (in $\mathrm{J}$ ) of potassium?

In order to comply with the requirement that energy be conserved, Einstein showed in the photoelectric effect that the energy of a photon $(h v)$ absorbed by a metal is the sum of the work function (\phi), which is the minimum energy needed to dislodge an electron from the metal's surface, and the kinetic energy $\left(E_{\mathrm{k}}\right)$ of the electron: $h \nu=\phi+E_{k}$. When light of wavelength $358.1 \mathrm{nm}$ falls on the surface of potassium metal, the speed (u) of the dislodged electron is $6.40 \times 10^{5} \mathrm{~m} / \mathrm{s}$
(a) What is $E_{\mathrm{k}}\left(\frac{1}{2} \mathrm{mu}^{2}\right)$ of the dislodged electron?
(b) What is $\phi$ (in $\mathrm{J}$ ) of potassium?

Key Concepts

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material, typically a metal, when it absorbs electromagnetic radiation such as light. It demonstrates the particle nature of light and forms a key piece of evidence for quantum mechanics since the energy of the incoming photons must be sufficient to overcome the material's binding forces.

Photon Energy

Photon energy is quantified by the equation E = h?, where h is Planck's constant and ? (or sometimes frequency) represents the frequency of the light. This concept underlines the quantization of electromagnetic radiation and is essential for linking the energy of light to its ability to dislodge electrons in the photoelectric effect.

Kinetic Energy of a Particle

The kinetic energy of a particle, especially an electron in this context, is given by the classical expression KE = ½ m u², where m is the mass of the electron and u is its velocity. This formula allows us to calculate the energy imparted to the electron as a result of its ejection from the metal surface.

Work Function

The work function is the minimum amount of energy required to remove an electron from the surface of a material. It represents the energy threshold that must be overcome by the absorbed photon energy for the electron to be emitted, linking the material properties to the observed effects in the photoelectric phenomenon.

Energy Conservation in Photoelectric Effect

Energy conservation in the photoelectric effect is expressed by the relationship that the energy of the incident photon is divided between overcoming the work function and providing kinetic energy to the emitted electron. This principle ensures that the total energy is accounted for during the emission process, emphasizing the interplay of quantum and classical physics.

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