Revision: Dual Nature of Matter and Radiation CUET (UG) Dual Nature of Matter and Radiation

It is a phenomenon where light falling on a material (usually a metal) causes it to emit electrons, generally called photoelectrons.

• Hertz (1887) observed that UV light falling on a metal cathode caused sparks to jump more easily across the gap of his oscillator.
• He noticed high voltage sparks were enhanced when the emitter plate was illuminated with UV light from an arc lamp.
• The phenomenon was later identified as the Photoelectric Effect — emission of electrons when light strikes a metal.
• Hertz also found that maximum spark length was produced when the apparatus was kept in a dark box, confirming light-induced emission.
• Hertz Experiment Setup: Oscillator with brass knobs joined by an induction coil; spark balls separated by a micrometre air gap and a ring receiver.

Hallwachs' Observation:

Hallwachs confirmed that UV light incident on a negatively charged zinc plate caused it to lose charge (emit electrons).

Lenard's Observations:

• Lenard measured electron kinetic energy vs light frequency.
• Found: Maximum KE of emitted electrons is directly proportional to the frequency of incident light.
• Changing the intensity of light had no effect on kinetic energy — only on the number of electrons emitted.
• Below a certain threshold frequency (ν₀), no electrons are emitted regardless of intensity.
• The photocurrent was directly proportional to the intensity of the incident light.
• Setup: cathode illuminated with light → electrons travel through vacuum → reach anode → current measured via ammeter.

• de Broglie (1924) Hypothesis: If radiation (waves) shows particle behaviour, then particles of matter should also show wave behaviour. This concept is called Matter Waves or de Broglie Waves.
• Nature's symmetry: electrons, protons, and neutrons can behave as waves under suitable conditions.

de Broglie Wave Equation:

For a particle of mass m moving with velocity v: \[\lambda=\frac{h}{p}=\frac{h}{mv}\]

Also written as: \[\lambda=\frac{h}{\sqrt{2mK.E}}\]

• Larger mass or velocity → smaller wavelength → harder to detect wave nature.
• For large (macroscopic) bodies, wavelengths are so tiny they cannot be measured — hence, no observable wave nature.

Experimental Proof of Matter Waves:

• Davisson and Germer experiment: Electrons showed diffraction patterns — direct proof of wave nature.
• G.P. Thomson's experiment also confirmed electron diffraction.
• Electrons have mass and move with definite velocity → can display wave-like behaviour.

Acceptance of Duality:

• Bohr's Law of Complementarity: Matter can be observed as either a particle or a wave, but not both simultaneously.
• Particle and wave aspects are complementary.

1.  The experiment verified the de-Broglie hypothesis.
2. In this experiment, the wave nature of electron particles was studied with the help of a nickel crystal.
3. Electrons undergo interference and diffraction phenomena and produce alternate bright and dark rings.
4. When accelerating potential V = 54 V:
   λ = 0.165 nm (Experimental value)
   λ = 0.167 nm (Theoretical value from de-Broglie hypothesis)