Question

Find the de-Broglie wavelength (inÅ) associated with an electron moving with a velocity 0.6c, where `c=3xx10^8 m//s` and rest mass of electron `=9.1xx10^(-31)kg, h=6.63xx10^(-34)Js`.

Answer 1

Rest mass of electron,
`m_0=9.1xx10^(-31)kg`
`v=0.6c=0.6xx3xx10^8=1.8xx10^8ms^-1`
As v is comparable to c, hence mass of the electron in motion will be a relativistic mass.
So, `m=(m_0)/(sqrt(1-v^2//c^2))=(m_0)/(sqrt(1-((0.6c)^2)/(c^2)))=(m_0)/0.8`
De-broglie wavelength,
`lambda=h/(mv)=h/((m_0//0.8)xxv)=(hxx0.8)/(m_0v)`
`=((6.6xx10^(-34))xx0.8)/((9.1xx10^(-31))xx(1.8xx10^8))`
`=0.322xx10^(-11)m=0.0322xx10^(-10)m`
`0.032Å`