A particle of mass `1 mg` has the same wavelength as an electron moving with a velocity of `3 xx 10^(6) ms^(-1)`. The velocity of the particle is

Options

A. `2.7 xx 10^(-18) ms^(-1)`
B. `9 xx 10^(-2) ms^(-1)`
C. `3 xx 10^(-31) ms^(-1)`
D. `2.7 xx 10^(-21) ms^(-1)`

Answer

A

Explanation

Wavelength of a particle is given by `lambda = (h)/(p)`
where `h` is Planck's constant.
wavelength of an electron is given by `lambda_(e) = (h)/(p_(e))`
but `lambda = lambda_(e)`
So , `p = p_(e )`
Putting the under given data
`m_(e ) = 9.1 xx 10^(-31) kg , v_(e ) = 3 xx 10^(6) m//s`,
`m = 1 mg = 1 xx 10^(-6) kg`
`v = (9.1 xx 10^(-31) xx 3 xx 10^(6))/( 1 xx 10^(-6))`
` = 2.7 xx 10^(-18) ms^(-1)`