Find the de-Broglie wavelength (in Å) assciated with a photon moving with a velocity 0.5 c, where `c=3xx10^(8)m//s`, rest mass of proton `=1.675xx10^(-27)kg, h=6.6xx10^(-34)Js`.

Answer

`2.27xx10^(-15) m`

Explanation

Rest mass proton `m_(0)=1.675xx10^(-27)kg`
`v=0.5 c=0.5xx(3xx10^(8))=1.5xx10^(8)m//s`
As v is comparable to c, hence mass of proton in motion will be a relative mass.
So, `m=(m_(0))/(sqrt(1-v^(2)//c^(2)))=(m_(0))/(sqrt(1-(0.5c)^(2)//c^(2))`
`=(m_(0))/(sqrt(0.75))=(2m_(0))/(sqrt(3))`
`lambda=h/(mv)=(6.63xx10^(-34))/((2m_(0)//sqrt(3))xxv)`
`=(6.6xx10^(-34)xxsqrt(3))/(2xx1.657xx10^(-27)xx(1.5xx10^(8)))`
`=2.27xx10^(-5)m`