travelling at same speeds, which of the following matter waves have the shortestwavelength?a) Alpha particleb) Protonc) Neutrond) Electron

The wavelength of a matter wave is given by the de Broglie equation:

λ = h / p

where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.

The momentum of a particle is given by:

p = mv

where m is the mass of the particle and v is the speed of the particle.

Given that all particles are travelling at the same speed, the particle with the smallest mass will have the smallest momentum and therefore the longest wavelength.

Looking at the list of particles:

a) Alpha particle - consists of 2 protons and 2 neutrons, so it has the greatest mass. b) Proton - has a mass of approximately 1 atomic mass unit (amu). c) Neutron - also has a mass of approximately 1 amu. d) Electron - has a mass of approximately 0.0005 amu.

Therefore, the electron has the smallest mass and will have the longest wavelength. Conversely, the alpha particle, having the greatest mass, will have the shortest wavelength. So, the answer is a) Alpha particle.