Single Choice

If travelling at same speeds, which of the following matter waves have the shortest wavelength?

AElectron
BAlpha particle ($$He^{2+}$$)
Correct Answer
CNeutron
DProton

Solution

According to de Broglie's equation
$$\lambda =\frac{h}{mv}$$
where, $$\lambda =$$ de-Broglie wavelength
$$h=6.626 \times 10^{−34}Js$$=Planck's constant
m=mass of particle
v= speed of particle
thus, for different particles travelling at same speed, the wavelength is inversely proportional to their masses
mass of electron = $$9.110 \times 10^{-28}$$ g
mass of proton = $$1.6727 \times 10^{-24}$$ g
mass of neutron = $$1.6750 \times 10^{-24}$$ g
mass of Alpha particles $$_4He^{2+} =4 \times$$ mass of proton=$$4 \times 1.6727 \times 10^{-24}=6.68 \times 10^{-24}$$g
Higher is the mass shorter will be the wavelength associated with it:
Therefore alpha particles having highest mass thus will have shortest wavelength.

SIMILAR QUESTIONS

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