explain why the maximum kinetic energy of photoelectrons is independent of intensity, whereas the photoelectric current is proportional to intensity

What’s happening when light hits a metal?

Light is made of tiny packets called photons. Each photon carries an energy

\$E = h\nu\$

where h is Planck’s constant and ν is the light’s frequency. When a photon strikes a metal surface, it can give its energy to an electron, freeing it from the metal.

But the electron doesn’t just take all the photon’s energy. Some of it is used to overcome the metal’s “work function” ϕ – the energy needed to escape. The rest becomes the electron’s kinetic energy:

\$K_{\text{max}} = h\nu - \phi\$

Think of a flashlight beam hitting a wall.

• Each photon is like a single ball of energy.
• Increasing the intensity (more photons per second) is like turning the flashlight on brighter – you get more balls, but each ball’s size stays the same.
• When a photon knocks an electron out, the maximum speed the electron can reach depends only on that single photon’s energy, not on how many photons are coming.

So, no matter how bright the light (high intensity), the fastest electrons you can get are limited by the photon’s energy minus the work function.

More photons = more electrons

The current is the flow of charge per unit time. If you shine a brighter light, you send more photons per second. Each photon that successfully ejects an electron contributes one electron to the current.

Mathematically:

\$I \propto \text{(number of photons per second)} \times e\$

where e is the electron charge. Thus, increasing intensity raises the number of electrons ejected per second, boosting the current.

Imagine a faucet that can turn on to let water flow. Each droplet of water is like a photon.

• Turning the faucet faster (higher intensity) releases more droplets per second.
• Each droplet has the same size (energy). If you drop a droplet onto a small stone, the stone’s speed after impact depends only on the droplet’s size, not on how many droplets you drop.
• But the total amount of stone that gets knocked over per minute increases with the number of droplets – just like the current increases with intensity.