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The dual nature of matter, proposed by Louis de Broglie, states that every moving particle (especially microscopic ones like electrons and protons) exhibits both particle and wave properties. This means such particles not only have mass and momentum but also an associated wavelength, known as de Broglie wavelength. This concept bridges classical mechanics and quantum mechanics and has been experimentally verified through phenomena like electron diffraction and interference. (A) The concept holds for all microscopic particles Correct. Dual nature has been observed in electrons, protons, neutrons, atoms, and even large molecules under suitable experimental conditions. (B) De Broglie wavelength is independent of particle's charge 
(C) Electron beam can show interference like light Correct. This was demonstrated in the Davisson-Germer experiment and the double-slit experiment, where electrons produced interference patterns , proving their wave nature. (D) Matter waves travel at speed equal to that of the particle Incorrect . The group velocity of the matter wave matches the particle’s velocity, but the phase velocity is generally different and can even exceed the speed of light. Thus, it is incorrect to say the wave travels at the same speed as the particle. Therefore, option (d) is the correct answer.
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