X rays of wavelength 2.63 were used to analyze a crystal. The angle of first-order diffraction (n = 1 in the Bragg equation) was 16.14°.
What is the spacing between crystal planes?(in pm)
Do I just plug everything in the Bragg's equation?
nλ=d*sinθ
n=1 ?
λ=263 pm?
I remember Bragg's equation being
n*lambda = 2d*sin theta.
oh that's right!
I still have a problem. I'm still getting the wrong answer
nλ=2d*sinθ
(1)*(263)/(2*sin(16.14))=d
-571.8=d
and the answer is suppose to be 479 pm
I think you punched in a wrong number somewhere. I get 473 something.
Yes, you are on the right track. To find the spacing between crystal planes, you can use Bragg's Law. The equation is:
nλ = d * sinθ
Where:
- n is the order of the diffraction (in this case, n = 1 for first-order diffraction)
- λ is the wavelength of the X-ray (given as 2.63 pm)
- d is the spacing between crystal planes (what we are trying to find)
- θ is the angle of diffraction (given as 16.14°)
So, plugging in the values we have:
1 * 2.63 pm = d * sin(16.14°)
Now, since sin(16.14°) is dimensionless, we can simplify the equation to:
2.63 pm = d * sin(16.14°)
To isolate d, divide both sides by sin(16.14°):
d = 2.63 pm / sin(16.14°)
Now you can calculate the value of d using a scientific calculator or a calculator that supports trigonometric functions: