An elementary particle is moving three times as fast as an electron. The ratio of the de broglie wavelengths of the particle and electron is `1.813 xx10^(-4)` . What is the mass of the particle ? ( Mass of electron `=9.1xx10^(-31) kg` )

Options

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

Answer

D

Explanation

Given : `(v)/(v_e) = 3 " and " (lamda)/(lamda_e) = 1.813 xx10^(-4)`
For the particle, `lamda = (h)/(mv) " or " m = (h)/(lamdav)`
For the electron, `lamda_e = (h)/(m_ev_e) therefore m_e = (h)/(lamda_e v_e)`
`therefore m/m_e = (h)/(lamdav) xx (lamda_ev_e)/(h) = (lamda_e/lamda) xx (v_e/v)`
`therefore m = (10^4)/(1.813) xx 1/3 xx 9.1xx10^(-31)`
`= 1.67xx 10^(-27) kg`