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 `1.813 xx 10^(-4)`. The mass of the particle is (Mass of electron = `9.1xx10^(-31)` kg )

Options

A. `1.67xx10^(-27)` kg
B. `1.67xx10^(-31)` kg
C. `1.67xx10^(-30)` kg
D. `1.67xx10^(-32)` kg

Answer

A

Explanation

de Broglie wavelength of a moving particle , having mass m and velocity v is given by
`lambda=h/p=h/(mv)` or `m=h/(lambdav)`
Given : `v/v_e=3, lambda/lambda_e=1.813xx10^(-4)`
Mass of the particle , `m=m_e(v_e/v)(lambda_e/lambda)`
Substituting the values , we get
`m=(9.1xx10^(-31) kg) xx (1/3) xx(1/(1.813xx10^(-4)))`
`rArr m=1.67xx10^(-27)` kg