A particle is moving three times as fast as an electron. The ratio of the de- Broglie wavelength of the particle to that of the electron is `1.813xx10^-4`. Calculate the particle's mass and identify the particle. Mass of electron `=9.11xx10^(-31)kg`.

Explanation

de Broglie wavelength of a moving particle, having mass m and velocity v:
`lambda=(h)/(p)=(h)/(mv)`
Mass, `m=h//v`
For an electron, mass `m_(e)=h//lambda_(e)v_(e)`
Now, we have `v//v_(e)=3` and
`lambda//lambda_(e)=1.813xx10^(-4)`
Then, mass of the particle, `m=m_(e)((lambda_(e))/(lambda))((v_(e))/(v))`
`m=(9.11xx10^(-31)kg)xx(1//3)xx(1//1.813xx10^(-4))`
`m=1.675xx10^(-27)kg`.
Thus, the particle, with this mass could be a proton or a neutron.