Light of wavelength 276 nm shines on a piece of magnesium metal. What is the speed of the eject

step 1 Let's calculate the speed of an injected electron from the surface of magnesium. The work functi

Light of wavelength 276 nm shines on a piece of magnesium...

Light of wavelength $276 \mathrm{~nm}$ shines on a piece of magnesium metal. What is the speed of the ejected electron? (Light energy greater than that of the work function of magnesium ends up as kinetic energy of the ejected electron. See Problem $7.76$ for the definition of work function and its value for magnesium.)

Key Concepts

Electron Speed Calculation

The speed of an ejected electron is determined using the relationship between kinetic energy and velocity, expressed by the equation K.E. = ½ m v², where m is the mass of the electron and v is its speed. By calculating the kinetic energy using the photon energy and the work function, the subsequent step involves solving for the electron’s speed.

Work Function

The work function is a characteristic property of a material that represents the minimum amount of energy required to eject an electron from its surface. It plays a critical role in the photoelectric effect, as only photons with energy exceeding the work function can release electrons, with any surplus energy being converted into the kinetic energy of the emitted electrons.

Kinetic Energy of the Ejected Electron

When a photon ejects an electron from a material, any energy in excess of the work function is converted into the kinetic energy of the electron. This kinetic energy determines how fast the electron will move and is a direct measure of the energy difference between the photon’s energy and the material’s work function.

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it is exposed to electromagnetic radiation of sufficient energy. It demonstrates that light can behave as particles (photons), each carrying a specific amount of energy, and that this energy must exceed the material’s work function in order for electrons to be liberated.

Photon Energy

Photon energy refers to the energy of a single light quantum, which is determined by its wavelength or frequency. It is calculated using the formula E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the photon. This concept is essential in determining whether the incident light has enough energy to overcome the work function of a material.

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