Animated Solution for Physics - Dual Nature of Matter and Radiation: The threshold wavelength for photoelectric emission from a material is $5200\text{ A˚}$. Photoelectrons will be emitted when this material is illuminated with monochromatic radiation from a

Imagine you are trying to knock a heavy ball out of a ditch. You can throw a million ping-pong balls at it, but it won't budge. However, a single, fast-moving bowling ball will knock it right out. This is the essence of the photoelectric effect!

The incident light provides this energy in discrete packets called photons. The energy of a photon is given by $E=\frac{hc}{\lambda }$.

Notice the inverse relationship: a smaller wavelength ($\lambda$) means a higher energy ($E$). The maximum wavelength that can just barely eject an electron is called the threshold wavelength (${\lambda }_0$). For emission to occur, our incident light must have a wavelength strictly less than this threshold:

This value sits comfortably in the visible spectrum (around the green region).

Now, let's look at our options: 1. Infrared (IR) Light: Infrared radiation has a longer wavelength than visible light, typically ${\lambda }_{\text{IR}}>7000\text{ A˚}$. Since ${\lambda }_{\text{IR}}>5200\text{ A˚}$, its photons are like the ping-pong balls—they simply don't have enough energy to eject an electron. 2. Ultraviolet (UV) Light: Ultraviolet radiation has a shorter wavelength than visible light, typically ${\lambda }_{\text{UV}}<4000\text{ A˚}$. Since ${\lambda }_{\text{UV}}<5200\text{ A˚}$, its photons are the bowling balls! They pack more than enough energy to cause photoemission.

The power of the lamp tells us about the intensity of the light—how many photons are emitted per second.

A $50\text{ W}$ infrared lamp shoots a massive number of low-energy photons, but none of them can eject an electron. A $1\text{ W}$ ultraviolet lamp shoots fewer photons, but every single one has enough energy to knock an electron out.

Therefore, both the $50\text{ W}$ and $1\text{ W}$ ultraviolet lamps will successfully cause photoelectric emission. The $50\text{ W}$ UV lamp will just eject more electrons per second than the $1\text{ W}$ UV lamp!