An X-ray tube operates at an unknown initial accelerating voltage V₀ . When the accelerating voltage is increased by 20 kV , the minimum wavelength of the continuous X-rays emitted becomes half of its initial value. The initial operating voltage V₀ is:

Step-by-step solution

The minimum wavelength of continuous X-rays is given by _ min = hc eV . Thus, the minimum wavelength is inversely proportional to the accelerating voltage: _ min 1 V . Let the initial voltage be V₀ and the new voltage be V_ new = V₀ + 20 kV . Given that the new minimum wavelength is half of the initial value, we have: _ new ₀ = V₀ V_ new = 1 2 V_ new = 2V₀ Substituting V_ new = V₀ + 20 kV : V₀ + 20 kV = 2V₀ V₀ = 20 kV . Confusing the X-ray cutoff wavelength with the de Broglie wavelength ( 1 V ) would incorrectly y