Discussion
The X-ray diffraction pattern of a monatomic cubic crystal with rigid spherical atoms of radius 1.56 Å shows several Bragg reflections of which the reflection appearing at the lowest \(2\theta\) value is from (111) plane. If the wavelength of X-ray used is 0.78 Å, the Bragg angle (in \(2\theta\), rounded off to one decimal place) corresponding to this reflection and the crystal structure, respectively, are
Answer: B
The reflection is at 2θ = 17.6°, and the crystal is face centered cubic.
In a cubic crystal the first reflection is (110) for body centered cubic and (111) for face centered cubic, so a lowest reflection from (111) means fcc. In fcc the atoms touch along the face diagonal, so 4r = a√2:
\[ \begin{aligned} a &= 2\sqrt{2}\,r = 2\sqrt{2} \times 1.56 = 4.41\ \text{\AA} \\ d_{111} &= a/\sqrt{3} = 2.55\ \text{\AA} \\ \sin\theta &= \frac{\lambda}{2d} = \frac{0.78}{5.10} = 0.153 \end{aligned} \]
So θ = 8.8° and 2θ = 17.6°. The option '8.8 and face centered cubic' gives θ, not 2θ. Both bcc options are ruled out because (111) is absent in bcc (h + k + l must be even).
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development