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.

Explanation

de Broglie wavelength of a moving particle, having mass m and velocity v :
`lambda=(h)/(p)=(h)/(mv)`
Mass, `m=h//lambda v`
For an electron, mass `=h//lambda_(e ) v_(e )`
Now, we have `m_(e )v//v_(e )=3` and
`lambda/lambda_(e )=1.813xx10^(-4)`
Then, mass of the particle, `m= me((lambda_(e ))/(lambda))((upsilon_(e ))/(upsilon))`
`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.