Animated Solution for Physics - Dual Nature of Matter and Radiation: In a photoelectric experiment, increasing the intensity of incident light

Imagine you are standing in front of a sturdy metal wall. This wall is packed with electrons, bound to the metal by an invisible force.

When light shines on this metal surface, something magical happens. If the light has enough energy, it can knock these electrons right out of the metal! This phenomenon is known as the photoelectric effect, and it completely revolutionized our understanding of physics.

In the classical wave theory of light, we used to think that increasing the brightness (or intensity) of light would simply hit the electrons with a bigger, more powerful wave, giving them more energy.

But the universe is far more interesting than that. Light actually behaves as a stream of tiny, discrete energy packets called photons.

Albert Einstein won the Nobel Prize for explaining this beautifully. He proposed that one photon interacts with exactly one electron.

He gave us the famous photoelectric equation:

Let's break this down. $K_{\text{max}}$ is the maximum kinetic energy of the ejected electron.

$h u$ represents the energy of the incoming photon, where $h$ is Planck's constant and $ u$ is the frequency of the light.

Finally, $\varphi$ is the work function, which is the minimum energy required to tear the electron away from the metal's grip.

This equation tells us a profound truth: the kinetic energy of the ejected electron depends only on the frequency of the incoming light and the nature of the metal itself.

Now, the question asks us what happens when we increase the intensity of the incident light.

This is where many students fall into a trap. In the quantum world, increasing the intensity of monochromatic light does not mean making the individual photons more energetic.

Think of photons as ping-pong balls being thrown at a wall. Increasing the frequency is like throwing the balls faster, with more energy.

But increasing the intensity is simply like throwing more ping-pong balls per second. The energy of each individual ball remains exactly the same.

So, what happens when we shine a more intense light on our metal surface?

Because there are more photons striking the metal every second, they will collide with more electrons. This means the number of ejected electrons will increase, which in turn increases the photoelectric current.

However, because the frequency $ u$ hasn't changed, the energy of each individual photon ($h u$) is still exactly the same.

Looking back at Einstein's equation, if $h u$ is constant and $\varphi$ is constant, then $K_{\text{max}}$ must also remain constant.

The kinetic energy of the ejected electrons does not care about how many photons are hitting the metal; it only cares about how energetic each individual photon is.

Therefore, increasing the intensity increases the number of incident photons, but the kinetic energy of the ejected electrons remains completely unchanged.

This perfectly matches option (d).