Dual Nature of Radiation and MatterNEET Physics · Class 12 · NCERT Chapter 11

Introduction

Two strands meet here. First, light, which we have so far treated as a wave, also behaves like a stream of particles called photons in the photoelectric effect. Second, particles such as electrons, which we have so far treated as little balls, also have a wave nature. Wave-particle duality is a hard idea, but the chapter runs on a small set of formulas you can drill.

Expect 1 to 2 NEET questions every year. Common asks: stopping potential vs frequency line, KE_max from Einstein's equation, de Broglie wavelength of an electron through a potential V, and photon momentum from wavelength.

Hertz and Lenard observations

Hertz (1887) noticed that UV light made a spark gap conduct more easily. Lenard (1902) refined the experiment. The findings:

• Above a certain threshold frequency f_0, light ejects electrons from a metal (photoelectric effect).
• Below f_0, no electrons come out, no matter how bright the light.
• Number of photoelectrons rises with intensity. Maximum kinetic energy depends on frequency, not intensity.
• Emission is essentially instantaneous (less than 10⁻⁹ s).

Classical wave theory could not explain any of these. Einstein (1905) did, by proposing that light comes in discrete packets called photons.

Work function and threshold

The minimum energy needed to free an electron from a metal's surface is the work function W_0. The corresponding photon frequency is the threshold:

Caesium W_0 ≈ 2.14 eV (visible light is enough); platinum W_0 ≈ 6.35 eV (only deep UV works).

Einstein's photoelectric equation

A photon of energy h f hits an electron in the metal. If h f > W_0, the electron escapes with maximum kinetic energy:

The same photon can never "split" between two electrons. One photon, one electron. KE_max depends only on the frequency and the metal, not on intensity.

Pick a metal and a light wavelength. If photon energy exceeds the work function, electrons are ejected with KE = h f - W_0. The stopping potential V_0 directly gives KE_max in volts.

Stopping potential

Apply a reverse voltage V to push photoelectrons back. The smallest V that just stops the most energetic ones is the stopping potential:

So V_0 in volts equals KE_max in electronvolts. Above f_0, V_0 grows linearly with f.

Stopping potential rises linearly with frequency. Slope is h/e (universal). x-intercept is the threshold frequency f_0 = W_0 / h (depends on the metal).

Photoelectric graphs

NEET tests three graphs. Recognise each:

• Photo-current vs applied voltage: rises and saturates. Three curves for three intensities (same f) saturate at different I_sat but cross V-axis at the same -V_0.
• Saturation current vs intensity: straight line through origin (I_sat ∝ Intensity).
• KE_max (or V_0) vs frequency: parallel lines for different metals. Slope = h. x-intercept = f_0.

Toggle between the three NEET-favourite photoelectric graphs.

Photons: energy and momentum

A photon is the quantum of EM radiation. Its energy and momentum:

Quick handle: E (in eV) × λ (in nm) ≈ 1240. So 620 nm light has photons of 2 eV; 124 nm UV has 10 eV photons.

Each photon carries energy E = h f and momentum p = h / λ. Quick mental check: E (in eV) × λ (in nm) ≈ 1240.

de Broglie wavelength of matter waves

Louis de Broglie (1924) proposed that matter, like light, has a wave nature. The wavelength is:

For everyday objects, λ is far too small to detect. For an electron at 100 eV, λ ≈ 0.123 nm, comparable to the spacing of atoms in a crystal, so it can show diffraction.

Every moving particle has a wave nature with λ = h / p. For everyday objects, λ is too small to detect; for electrons it is comparable to atomic spacings.

Electron accelerated through V volts

An electron starting at rest accelerated through V volts gains KE = eV. Its de Broglie wavelength:

At V = 100 V, λ = 1.23 Å. At V = 10 kV (electron microscope), λ = 0.123 Å. The shorter the wavelength, the finer the detail you can image. That is why electron microscopes outperform light microscopes.

An electron starting at rest accelerated through V volts gains KE = eV. Its de Broglie wavelength is: λ = 12.27 / √V Å.

Davisson-Germer experiment

Davisson and Germer (1927) accelerated electrons through 54 V and scattered them off a nickel crystal. They found a sharp diffraction peak at scattering angle 50°. Using Bragg's law for nickel (d = 0.91 Å), the peak corresponds to wavelength 1.65 Å. de Broglie's formula gave 12.27 / √54 = 1.67 Å. Match. Matter waves are real.

This is the first direct experimental proof of the wave nature of electrons.

Wave-particle duality and a comparison

Both light and matter show wave behaviour (interference, diffraction) and particle behaviour (photons, point impacts). For a fixed energy, a photon is much "wider" than an electron because c is huge. For a fixed momentum, both have the same λ.

For the same energy, a photon and an electron have very different wavelengths. The photon is much "wider" because it travels at c, while the electron moves much more slowly.

Worked NEET problems

Summary cheat sheet

• Einstein: $h\nu =W_0+{\text{KE}}_{\max }$.
• Stopping potential: $e{V}_0={\text{KE}}_{\max }$.
• Threshold: $f_0=W_0/h$, ${\lambda }_0=hc/W_0$.
• Quick: E (eV) × λ (nm) ≈ 1240.
• Photon: E = hν, p = h/λ = E/c.
• de Broglie: $\lambda =h/p=h/\sqrt{2m{E}_k}$.
• Electron through V: $\lambda =12.27/\sqrt{V}\text{A˚}$.
• I_sat: ∝ intensity. V_0: ∝ frequency (above f_0).
• V_0 vs f slope: h/e (universal).

Next: try the interactive widgets for the photoelectric equation, V_0-f line and de Broglie wavelength, or work through the 30 NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.