Question

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

• A. Electron
• B. Alpha particle ($H{e}^{2+}$)
• C. Neutron
• D. Proton

Answer 1

The correct option is B Alpha particle ($H{e}^{2+}$)

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 ${}_{4}H{e}^{2+}=4\times$ 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.