Animated Solution for Physics - Dual Nature of Matter and Radiation: The potential difference applied to an X-ray tube is increased. As a result, in the emitted radiation

Voltage, Wavelength, and Intensity

Imagine you are looking inside an X-ray tube. It is a fascinating piece of technology where high-speed physics meets electromagnetic radiation. When we apply a potential difference, let's call it $V$, across the tube, the electrons emitted from the cathode are accelerated towards the anode target. During this journey, they gain a kinetic energy equal to $K=eV$.

Now, what happens when these high-speed electrons smash into the target? Their kinetic energy is rapidly decelerated, and this lost energy is converted into X-ray photons. This process produces a continuous spectrum of X-rays known as Bremsstrahlung, or "braking radiation."

Let's think about the most energetic photon that can possibly be produced in this setup. This extreme case happens if an electron loses all of its kinetic energy in a single, head-on collision with a target atom.

So, the maximum energy of the resulting photon, $E_{\text{max}}$, is exactly equal to the electron's kinetic energy, $eV$. Since the energy of a photon is inversely proportional to its wavelength ($E=\frac{hc}{\lambda }$), this maximum energy corresponds to the minimum possible wavelength. We call this the cut-off wavelength, ${\lambda }_{\text{min}}$.

The question asks what happens when we increase the potential difference $V$. Look closely at our equation for ${\lambda }_{\text{min}}$. The voltage $V$ is in the denominator. If the denominator gets larger, the overall value of the fraction must get smaller.

Therefore, the minimum wavelength ${\lambda }_{\text{min}}$ decreases. On a graph of Intensity versus Wavelength, the entire spectrum shifts to the left, starting from a shorter wavelength.

But what about the intensity of the X-rays? This is where many students get tripped up. Intensity isn't just about the raw number of photons; it is defined as the total energy emitted per unit area per unit time.

Because we increased the voltage, the photons being emitted now have higher maximum energies. So, even if the tube emits the exact same number of photons per second (which depends on the filament current, not the accelerating voltage), the total energy those photons carry is significantly greater.

This means the overall intensity of the radiation increases.

By cranking up the voltage on our X-ray tube, we've caused two distinct changes: 1. The intensity of the emitted radiation has increased because the individual photons are more energetic. 2. The minimum wavelength has decreased because the maximum possible photon energy is higher.

Looking at our options, this means both (a) and (d) are the correct choices.