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//lambdav`
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.