1.

A particle is moving three times as fast as anelectron. 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 )

Answer»

`1.67xx10^(-27)` kg
`1.67xx10^(-31)` kg
`1.67xx10^(-30)` kg
`1.67xx10^(-32)` kg

Solution :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


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