One of the spectral lines emitted by excited `He^(+)` ions has a wavelength `lambda = 410 nm`. Find the soppler shift `Delta lambda` of that line when observed at an angle `theta = 30^(@)` to the beam of moving ions possessing kinetic energy `T = 10MeV`.

Explanation

`(Deltav)/(v) = (v)/(c ) cos theta` from the previous problem But `v lambda = c` gives an differentiation
`(Deltav)/(v) =- (Deltalambda)/(lambda)`
So `Delta lambda =- lambda sqrt((v^(2))/(c^(2))) cos theta =- lambda sqrt((2T)/(mc^(2))) cos theta`
on using `T=(1)/(2)mv^(2), m = mass` of `He^(+)`ion
We use `mc^(2) = 4 xx 938MeV`. Putting other values
`Delta lambda =- 26 nm`