Directions : In the following questions, A statement of Assertion (A)...
De-Broglie wavelength, λ = h/mv h and v remaining constant, λ ∝ 1/m So, as the mass of the particle becomes smaller and smaller the de-Broglie wavelength of the particle becomes more and more significant.
Hence, assertion and reason both are true and reason explains the assertion properly.
Directions : In the following questions, A statement of Assertion (A)...
Assertion: de-Broglie equation is significant for microscopic particles.
Reason: de-Broglie wavelength is inversely proportional to the mass of a particle when velocity is kept constant.
The correct answer is option 'A', which means both the assertion and the reason are true, and the reason is the correct explanation of the assertion.
Explanation:
The de-Broglie equation is a fundamental equation in quantum mechanics that relates the wavelength of a particle to its momentum. It was proposed by Louis de Broglie and is given by the equation:
λ = h / p
where λ is the de-Broglie wavelength, h is the Planck's constant, and p is the momentum of the particle.
The de-Broglie wavelength is significant for microscopic particles because it demonstrates the wave-particle duality of matter. According to quantum mechanics, particles such as electrons, protons, and neutrons exhibit both particle-like and wave-like properties.
The reason provided in the statement is that the de-Broglie wavelength is inversely proportional to the mass of a particle when velocity is kept constant. This can be derived from the de-Broglie equation.
If we rearrange the equation as:
p = h / λ
Since the velocity of a particle is given by v = p / m, where m is the mass of the particle, we can substitute the expression for momentum:
v = (h / λ) / m
Rearranging this equation gives us:
λ = h / (m * v)
From this equation, it is clear that the de-Broglie wavelength is inversely proportional to the mass of the particle when the velocity is kept constant. This means that lighter particles have longer wavelengths compared to heavier particles when their velocities are the same.
Therefore, both the assertion and the reason are true, and the reason correctly explains why the de-Broglie equation is significant for microscopic particles.