The wavelength (in m ) of a particle of mass `11.043xx 10^(-26)` kg moving with a velocity of `6.0xx10^7 ms^(-1)` is

Options

A. `1.0xx10^(16)`
B. `6.0xx10^(-16)`
C. `1.0xx10^(-16)`
D. `6.0xx10^(16)`

Answer

C

Explanation

Wavelength `=("Planck s constant")/("Momentum")=(h)/(m)`
But, momentum `=sqrt(2Em)`
`:." "lambda=(h)/(sqrt(2Em))=(h)/(sqrt(2xx(1)/(2)mv^(2)xxm))lambda=(h)/(mv)`
Given, mass of the particle = m
`=11.043xx10^(-26)" kg"`
Velocity of particle `=v=6.0xx10^(7)" ms"^(-1)`
Planck's constant `=h=6.626xx10^(-34)" J-s"`
Substituting these values, we get
`lambda=(6.626xx10^(-34)" Js")/(11.043xx10^(-26)xx6.0xx10^(7))`
`=(6.626xx10^(-34))/(6.626xx10^(-18))=1.0xx10^(-16)" m"`