A KE derivation from Compton Effect

[Pengwuino]

I have an odd problem here. I need to show that:

KE = \frac{{\frac{{\Delta \lambda }}{\lambda }}}{{1 + (\frac{{\Delta \lambda }}{\lambda })}}hf

I've basically derived KE = \frac{{hc}}{{\lambda _o }} - \frac{{hc}}{{\lambda '}} down to…

KE(\frac{{\lambda '}}{{\lambda _o ^2 }}) = (\frac{{\Delta \lambda }}{{\lambda _o }})hf

but I'm not sure how I can turn that \frac{{\lambda '}}{{\lambda _o ^2 }} into a 1 + (\frac{{\Delta \lambda }}{{\lambda _o }})

Can anyone help?

 

[phucnv87]

\Delta E=\frac{hc}{\lambda_0}(1-\frac{\lambda_0}{\lambda})

1-\frac{\lambda_0}{\lambda}=\frac{\lambda-\lambda_0}{\lambda}=\frac{\frac{\lambda-\lambda_0}{\lambda_0}}{1+\frac{\lambda-\lambda_0}{\lambda_0}}

Consider \frac{\Delta \lambda}{\lambda_0}=\frac{\lambda-\lambda_0}{\lambda_0}

And we have the answer[/color]

 

[Pengwuino]

Alright i'll try to get to that myself... is there anything special about the equation they wanted me to find?