Master JEE Main Mock Tests for Dual Nature of Matter & Radiation (2025-26)

The main postulates of de Broglie's hypothesis are:
• All material particles have an associated wavelength, known as the de Broglie wavelength (λ).
• The wavelength is given by λ = h/p, where h is Planck's constant and p is momentum.
• This wave-particle duality applies to electrons, protons, and all microscopic as well as macroscopic objects, but is significant only for particles with small mass and high velocity.

The photoelectric effect is the emission of electrons from a metal surface when it is exposed to light. It supports the particle nature of light because:
• Electrons are ejected only if the frequency of light is above a certain threshold.
• The kinetic energy of the emitted electrons depends on the frequency, not the intensity, of incident light.
• It is explained using photons, where each photon has energy E = hν.

The mathematical expression for de Broglie wavelength is λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. This relation shows that every moving particle has a wave character, which is especially significant for microscopic particles like electrons.

The Davisson-Germer experiment experimentally confirmed the wave nature of electrons by demonstrating electron diffraction on a nickel crystal. This was a pivotal experiment validating de Broglie's hypothesis and demonstrated that particles like electrons can exhibit wave properties such as interference and diffraction.

For macroscopic objects, the de Broglie wavelength (λ = h/p) is extremely small due to their large mass. Therefore, their wave properties cannot be observed or measured practically. The wave nature is noticeable only for microscopic particles like electrons, protons, and neutrons.

The threshold frequency (ν₀) is the minimum frequency of incident light below which no photoelectric emission occurs from a metal surface, regardless of the intensity of light. The energy of photons must be at least equal to the work function of the metal to release electrons.

The main differences between wave nature and particle nature are:
• Particle nature: Exhibits mass, discrete energy, and localized position.
• Wave nature: Shows interference, diffraction, and extended in space.
• Both natures are necessary to fully describe phenomena at atomic and subatomic scales.

The work function (φ) is the minimum energy required to remove an electron from the surface of a metal. In the photoelectric effect, only photons with energy greater than or equal to the work function can cause the ejection of electrons from a metal surface.

The dual nature of matter, particularly the wave nature of electrons, allows electron microscopes to achieve high resolution. Electrons have short de Broglie wavelengths, enabling them to resolve objects much smaller than what is possible with visible light due to their wave properties.

पदार्थ और विकिरण की द्विक प्रकृति से तात्पर्य है कि दोनों, अर्थात प्रकाश (विकिरण) और पदार्थ, में तरंग और कण दोनों के गुण होते हैं। उदाहरण के लिए, इलेक्ट्रॉन में तरंग व्यवहार (जैसे, विवर्तन) और कण व्यवहार (जैसे, टक्कर) दोनों देखे जाते हैं।

In JEE mock tests for Dual Nature of Radiation and Matter, students can expect:
• Conceptual MCQs on photoelectric effect and de Broglie's hypothesis.
• Numerical problems on calculating de Broglie wavelength.
• Assertion-reason and statement-type questions on wave-particle duality.
• Theory-based and application-type questions derived from NCERT and previous JEE exams.