In an X-ray setup, increasing the voltage _________ the wavelength.

In an X-ray setup, increasing the voltage decreases the wavelength of the emitted X-rays. This relationship is fundamentally based on the physics of X-ray production. When electrons are accelerated through a higher voltage, they gain more kinetic energy. Upon colliding with the target material in the X-ray tube, this energy is converted to electromagnetic radiation in the form of X-rays.

According to the principles of wave-particle duality in physics, the energy of the emitted X-ray photons is inversely related to their wavelength. The higher the energy (which increases with higher voltage), the shorter the wavelength of the X-rays produced. This occurs because the energy of a photon can be described by the equation E = h * f, where E is energy, h is Planck’s constant, and f is frequency. Since frequency and wavelength are inversely related (as expressed in the equation c = λ * f, where c is the speed of light and λ is wavelength), an increase in frequency (resulting from the increase in energy) directly leads to a decrease in wavelength.

Therefore, when voltage is increased in an X-ray setup, the wavelength of the emitted X-rays decreases, making this the correct answer.