An electron and an alpha particle (a helium-4 nucleus)each have the same non-relativistic speed.Which has the greatest kinetic energy,and which has the shortest de Broglie wavelength?
A)the alpha particle,the alpha particle
B)the alpha particle,the electron
C)the electron,the alpha particle
D)the electron,the electron

Question

Quizplus · Accepted Answer

The kinetic energy of a particle is given by the formula: 
KE = (1/2)mv^2 
where m is the mass of the particle and v is its velocity. 
Since the alpha particle has a much greater mass than the electron, it will have a much greater kinetic energy at the same speed.

The de Broglie wavelength of a particle is given by the formula: 
λ = h/p 
where h is Planck's constant and p is the momentum of the particle. 
Since the momentum of a particle is given by p = mv, the de Broglie wavelength is proportional to the mass and inversely proportional to the velocity. 
Therefore, the electron with its smaller mass will have a shorter de Broglie wavelength than the alpha particle at the same velocity.

An Electron and an Alpha Particle (A Helium-4 Nucleus)each Have