In an X-ray tube, electrons accelerated through a potential difference of 15, 000 V strike a copper

Q: Why is the 15,000 V given in the question if we don't use it?

It's a classic distractor! Examiners often provide extra information to test if you truly understand the concepts or if you just blindly plug numbers into formulas.

Q: What if the question asked for the speed of the electron?

Then you would use the 15,000 V. The kinetic energy gained by the electron would be $K = eV$, and you could find its speed using $K = \frac{1}{2}mv^2$.

Q: Does the speed of the X-ray change if we use a different target like Tungsten instead of Copper?

No. The speed of an electromagnetic wave in a vacuum is a universal constant, $c = 3 \times 10^8 \text{ m/s}$, regardless of how it was produced or what target was used.

Q: Does the 15,000 V affect the X-ray at all?

Yes, it affects the *energy* (and thus the frequency and wavelength) of the emitted X-ray photons. A higher voltage produces more energetic (harder) X-rays, but they still travel at the speed of light.

Q: Is the speed exactly $3 \times 10^8 \text{ m/s}$ inside the tube?

Yes, because the inside of an X-ray tube is a highly evacuated chamber (a vacuum). In a vacuum, all EM waves travel at exactly $c$.

Question

In an X-ray tube, electrons accelerated through a potential difference of 15, 000 V strike a copper target. The speed of the emitted X-ray inside the tube is ....... m/s.

Sigma Percentile · Accepted Answer

Imagine you are sitting in the exam hall, the clock is ticking, and you come across this question. You see a voltage of $15,000 	ext{ V}$, an electron, and a copper target. Your brain immediately fires up the kinetic energy formula: $K = eV$. You might even start calculating the velocity of the electron using $\frac{1}{2}mv^2 = eV$.

But wait! Take a deep breath and read the question one more time.

### The Trap of Extra Information

The question asks for the speed of the **emitted X-ray**, not the electron! This is a classic trap set by examiners. They provide extra, seemingly crucial information—like the $15,000 	ext{ V}$ potential difference and the copper target—to see if you will blindly plug numbers into a formula or if you truly understand the physical reality of the setup.

The voltage is indeed real; it is used to accelerate the electrons from the cathode so they smash into the copper target with high kinetic energy. When these high-speed electrons decelerate upon hitting the target, their kinetic energy is converted into X-ray photons.

### The Nature of X-Rays

So, what exactly is an X-ray? An X-ray is simply a high-energy electromagnetic wave. It belongs to the same family as the visible light you use to see, the microwaves you use to heat your food, and the radio waves that carry signals to your phone.

One of the most beautiful and fundamental laws of physics is that **all electromagnetic waves travel at the exact same speed in a vacuum**. It doesn't matter if it's a low-energy radio wave or a highly energetic X-ray produced by a $15,000 	ext{ V}$ potential difference.

### The Universal Speed Limit

Inside the evacuated chamber of an X-ray tube, these emitted X-rays travel at the universal speed limit: the speed of light, denoted by $c$.

$$v = c = 3 	imes 10^8 	ext{ m/s}$$

The voltage determines the *energy* and the *wavelength* of the X-rays, but it has absolutely zero effect on their speed. By recognizing this fundamental concept, you can bypass the trap entirely and arrive at the correct answer in seconds. Trust your core concepts!

Animated Solution for Physics - Electromagnetic Waves: In an X-ray tube, electrons accelerated through a potential difference of 15, 000 V strike a copper target. The speed of the emitted X-ray inside the tube is ....... m/s.

Visualized Solution

$V = 15, 000 V$

$K = e V$

$X-rays$

$v = c$

$3 \times 1 0^{8} m/s$

The Sigma Insight: Characteristics of Electromagnetic Waves

The Trap of Extra Information

The Nature of X-Rays

The Universal Speed Limit

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