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 `upsilon`:
` lambda = h/p = h/(mv)`
Mass, m = `h//lambda`
For an electron , mass `m_(e) = h//lambda _(e)v_(e)`
Now, we have `v//v_(e) = 3` and
`lambda//lambda_(e) =1.813 xx 10^(-4)`
Then , mass of the particle ,
` m = m_(e) ((lambda_(e))/lambda) ((v_(e))/v)`
` m = (9.11 xx 10^(-31)kg)xx (1//3) xx (1//1.813 xx 10^(-4))`
` m = 1.675 xx 10^(-27)` kg
Thus, the particle , with this mass could be a proton or a neutron .