X-ray Diffraction: First-Order Bragg & 2nd Order Angles

[The_Fritz]

Homework Statement

First-order Bragg diffraction is observed at 25.9degrees relative to the crystal surface, with spacing between atoms of 0.26 nm.
a)What is the wavelength of the X-rays?
b)At what angle will second order be observed?

Homework Equations

m$$\lambda$$=2dsin$$\phi$$

The Attempt at a Solution

I solved part b: $$\lambda$$=(2dsin$$\phi$$)=(2(.26*10^-9 m)(sin25.9deg)=.23nm which is correct.
For part a I tried: sin$$\phi$$=(m$$\lambda$$)/(2d)=((2)(.23*10^-9 m))/((2)(.26*10^-9))=62.2 Which is apparently close because mastering physics says,"Not quite. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures." Please help! I am down to one attempt and need to get it right this time. Thx!

 

[ideasrule]

The answer to a) isn't 0.23nm; it's 0.22713692995120516100900531927073 nm. If you want to get an answer for b) that's accurate to 3 significant digits, you should use at least 4, preferably 5, of those digits.