In a color TV tube, electrons are accelerated through a...

In a color TV tube, electrons are accelerated through a potential difference of $20.0 \mathrm{kV}$. Some of the electrons strike the metal mask (instead of the phosphor dots behind holes in the mask), causing $x$ -rays to be emitted. What is the smallest wavelength of the $\mathrm{x}$ -rays emitted?

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Key Concepts

Electron Kinetic Energy

When electrons are accelerated through a potential difference, they gain kinetic energy equal to the product of their charge and the voltage (E = qV). This concept is fundamental in understanding how potential energy is converted into kinetic energy, which then can be used to generate radiation when the electrons interact with matter.

Photon Energy-Wavelength Relationship

The energy of a photon is related to its wavelength by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This inverse relationship means that higher energy photons have shorter wavelengths, a principle that is crucial when calculating the minimum wavelength (or maximum energy) of x-rays produced in such processes.

X-ray Production (Bremsstrahlung Radiation)

In x-ray tubes, high-energy electrons strike a metal target, and a fraction of their kinetic energy is converted into x-rays through a process called Bremsstrahlung radiation. The smallest wavelength of the x-rays corresponds to the case where an electron's entire kinetic energy is converted into a single photon, setting the cutoff wavelength by the relation ?_min = hc/(eV).

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