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. `2.7xx10^(-18)" m"//"s"`
B. `9xx10^(-2)" m"//"s"`
C. `3xx10^(-31)" m"//"s"`
D. `2.7xx10^(-21)" m"//"s"`

Answer

A

Explanation

Wavelength of a particle is given by
`lambda=(h)/(p)`
where h is Planck's constant and wavelength of an electron is given by
`lambda_(e)=(h)/(p_(e))`
but `" "lambda=lambda_(e)`
So, `" "p=p_(e)`
or `" "mv=m_(e)v_(e)`
or `" "v=(m_(e)v_(e))/(m)`
Putting the under given data
`m_(e)=9.1xx10^(-31)"kg",`
`v_(e)=3xx10^(6)"m"//"s",`
`m=1mg=1xx10^(-6)kg`
`v=(9.1xx10^(-31)xx3xx10^(6))/(1xx10^(-6))`
`=2.7xx10^(-18)" m"//"s"`