CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

In Fig. $$ 36-48, $$ let a beam of x rays of wavelength $$ 0.125 \mathrm{nm} $$ be incident on an $$ \mathrm{NaCl} $$ crystal at angle $$ \theta=45.0^{\circ} $$ to the top face of the crystal and a family of reflecting planes.
Let the reflecting planes have separation $$ d=0.252 \mathrm{nm} . $$ 
The crystal is turned through angle $$ \phi $$ around an axis perpendicular to the plane of the page until these reflecting planes give diffraction maxima.
What are the
(a) smaller and
(b) larger value of $$ \phi $$ if the crystal is turned clockwise and the
(c) smaller and
(d) larger value of $$ \phi $$ if it is turned counterclockwise?
1778898_8227fd85222149e89cca61e11aa5772c.png


Solution

We want the reflections to obey the Bragg condition 
$$ 2 d \sin \theta=m \lambda $$, where $$ \theta $$ is the angle between the incoming rays and the reflecting planes, $$ \lambda $$ is the wavelength, and $$ m $$ is an integer. 
We solve for $$ \theta $$
$$\theta=\sin ^{-1}\left(\dfrac{m \lambda}{2 d}\right)=\sin ^{-1}\left(\dfrac{\left(0.125 \times 10^{-9} \mathrm{m}\right) m}{2\left(0.252 \times 10^{-9} \mathrm{m}\right)}\right)=0.2480 \mathrm{m}$$
(a) For $$ m=2 $$ the above equation gives $$ \theta=29.7^{\circ} . $$ 
The crystal should be turned
$$\phi=45^{\circ}-29.7^{\circ}=15.3^{\circ} \text { clockwise }$$
(b) For $$ m=1 $$ the above equation gives $$ \theta=14.4^{\circ} . $$ 
The crystal should be turned
$$\phi=45^{\circ}-14.4^{\circ}=30.6^{\circ} \text { clockwise }$$
(c) For $$ m=3 $$ the above equation gives $$ \theta=48.1^{\circ} . $$ 
The crystal should be turned
$$\phi=48.1^{\circ}-45^{\circ}=3.1^{\circ} \text { counterclockwise. }$$
(d) For $$ m=4 $$ the above equation gives $$ \theta=82.8^{\circ} . $$ 
The crystal should be turned
$$\phi=82.8^{\circ}-45^{\circ}=37.8^{\circ} \text { counterclockwise }$$
Note that there are no intensity maxima for $$ m>4, $$ as one can verify by noting that $$ m \lambda /2 d $$ is greater than 1 for $$ m $$ greater than 4

Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image