If the particles are moving with same velocity, then maximum de-Broglie wavelength is for

Explanation:

de-Broglie Wavelength of Particles:

• de-Broglie wavelength is given by the formula: λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.
• The momentum p is defined as p = mv, where m is the mass of the particle and v is its velocity.
• Since all particles are moving with the same velocity, the de-Broglie wavelength is inversely proportional to the mass of the particle.
• The particle with the least mass will have the maximum de-Broglie wavelength for a given velocity.

Out of the listed particles, the β-particle (which is an electron) has the least mass. As the de-Broglie wavelength is inversely proportional to the mass, the β-particle will have the maximum de-Broglie wavelength compared to the proton, neutron, and α-particle, which all have larger masses.

The correct answer is: β-particle.