Find the de-Broglie wavelength associated with an electron moving with a velocity 0.5 c and rest mass = `9.1 xx 10^(-31) kg`.

Explanation

Given , rest mass , `m_0=9.11xx10^(-31) kg`
Velocity of electon , `v=1/2c=(3xx10^8)/2=1.5xx10^8"m//s"^2`
Mass of the electron in motion is
`m=m_0/(sqrt(1-v^2/c^2))=m_0/(sqrt(1-((1/2c)/c)^2))=m_0/sqrt(1-0.25)`
`=m_0/sqrt0.75`
`=(9.11xx10^(-31))/(0.86)`
`=10.6xx10^(-31)kg`
The de Broglie wavelength associated with electon is
`lamda=h/(mv)=(6.6xx10^(-34))/(10.34xx10^(-31)xx1.5xx10^8)`
`=4.16xx10^(-12)m`