Which of the following atoms would have the longest de Broglie wavelength, if all have the same velocity? A) Li
B) Na
C) Fe
D) Pb
E) Not possible to tell with given information

The atom that have the longest de Broglie wavelength is ; ( A ) Li

Wave particle duality is a phenomenon by de Broglie. that shows that The wavelength associated with matter waves is related to its mass and velocity .

Wave particle duality is represented as ;  λ = h / mv

λ= wavelength of matter waves

m= mass of the particle

v= velocity of the particle

Given that the elements have the same velocity the atom that would have the longest de Broglie wavelength is Li

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Li

Explanation:

The phenomenon of wave particle duality was well established by Louis deBroglie. The wavelength associated with matter waves was related to its mass and velocity as shown below;

λ= h/mv

Where;

λ= wavelength of matter waves

m= mass of the particle

v= velocity of the particle

This implies that if the velocities of all particles are the same, the wavelength of matter waves will now depend on the mass of the particle. Hence; the wavelength of a matter wave associated with a particle is inversely proportional to the magnitude of the particle's linear momentum. The longest wavelength will then be obtained from the smallest mass of matter. Hence lithium which has the smallest mass will exhibit the longest DeBroglie wavelength