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. ` 1.67 xx 10^(-27) kg `
B. ` 1.67 xx 10^(-31) kg `
C. ` 1.67 xx 10^(-30 ) kg `
D. ` 1.67 xx 10^(-32) kg `

Answer

A

Explanation

de Broglie wavelength of a moving particle , having mass m and velocity v is given by
`lamda = h / p = (h) /(mv) " or " m = (h)/(lamdav)`
For an electron
`lamda_e=h/(m_ev_e)" or " m_e=h/(lamda_ev_e)`
Given : `v/v_e = 3 , lamda/lamda_e = 1.813 xx10^(-4)`
Mass of the particle , `m = m_e (v_e/v) (lamda_e/(lamda))`
Substituting the values , we get
`m=(9.1 xx10^(-31)kg)xx(1/3)xx(1/(1.813 xx10^(-4)))`
`m = 1.67 xx 10^(-27) kg `