Question

A free He nucleus (consisting of 2 protons and 2 neutrons) and a free proton have...

A free He nucleus (consisting of 2 protons and 2 neutrons) and a free proton have the same

speed. This means that, compared to the matter wave associated with the proton, the matter

wave associated with the He nucleus:

a. has a longer deBroglie wavelength and a smaller kinetic energy

b. has a longer deBroglie wavelength and a greater kinetic energy

c. has the same deBroglie wavelength and the same kinetic energy

d. has a shorter deBroglie wavelength and a smaller kinetic energy

e. has the shorter

deBroglie wavelength and a greater kinetic energy

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Answer #1

Answer will be option e.) has the shorter deBroglie wavelength and a greater kinetic energy

As,

Mass of He nucleus = 4 times the mass of proton (u)

Charge of He nucleus = 2 times the charge of the proton (+e)

Velocity same for both the particle.

They both have same velocity so that higher the mass higher the kinetic energy hence

K.E(He nucleus) is greater than K.E of free proton.

Also for the wavelength we have,

Lambda = h/mv

As velocity is constant here so that higher the mass lower the wavelength of the particle. And here mass of He nucleus is higher so its wavelength will ve shorter than the wavelength of the proton.

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