<DIV>In a Compton scattering experiment, the incident X-rays have a wavelength o

Question

<DIV>In a Compton scattering experiment, the incident X-rays have a wavelength of <FONT color=#dd0000>0.2650</FONT> nm, and the scattered X-rays have a wavelength of <FONT color=#dd0000>0.2677</FONT> nm. Through what angle <SPAN><EM>?</EM></SPAN> in the figure are the X-rays scattered?<BR>_________°<BR>
<DIV class=figure><IMG alt="" src="http://www.webassign.net/CJ/29-10fig.gif" src_cetemp="http://www.webassign.net/CJ/29-10fig.gif"></DIV></DIV>

Explanation / Answer

incident wavelength w = 0.265 nm = 0.265 * 10^-9 m Scatterred wavelength w ' = 0.2677 nm = 0.2677* 10^ -9 m we know compton shift w ' - w = ( h / mc ) ( 1-cos (theta)) where h = planck's constant = 6.625 * 10^ -34 J s c = speed of light = 3* 10^ 8 m / s m = mass of electron = 9.11* 10^ -31 kg plug the values we get 2.7 * 10^-12 = 2.424* 10^ -12 * ( 1- cos ( theta) ) 1.113 = 1-cos ( theta) cos( theta ) = 1-1.113 = -0.113 theta = 96.53 degrees

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