If the radius of the octachedral void is r and radius of the atoms in close packing is R, derive relation between r and R.

 

 

 

Question 1.10) Calculate the efficiency of packing in case of a metal crystal for (i) simple cubic (ii) body-centred cubi

Question 1.10) Calculate the efficiency of packing in case of a metal crystal for

(i) simple cubic

(ii) body-centred cubic

(iii) face-centred cubic (with the assumptions that atoms are touching each other).

Answer:

 

(i) Simple cubic

In a simple cubic lattice, the particles are located only at the corners of the cube and touch each other along the edge.

Let the edge length of the cube be ‘a’ and the radius of each particle be r.

So, we can write:

a = 2r

Now, volume of the cubic unit cell $=a^3$

$={\left(2r\right)}^3$

$=8r^3$

We know that the number of particles per unit cell is 1.

Therefore, volume of the occupied unit cell

$=\frac{4}{3}\pi r^3$

 

packing efficiency =$\frac{Volume of the one particle}{Volume of cubic unit cell}\times 100\%$

$\frac{{\displaystyle \frac{4}{3}}\pi r^3}{8r^3}\times 100\%$

$=\frac{1}{6}\pi \times 100\%$

$=\frac{1}{6}\mathit{\times }\frac{\mathit{22}}{\mathit{7}}\times 100\%$

=52.4%

 

(ii) Body-centred cubic

It can be observed from the above figure that the atom at the centre is in contact with the other two atoms diagonally arranged.

From ΔFED

$b^2=a^2+a^2$

${\mathrm{b}}^2=2{\mathrm{a}}^2$

$b=\sqrt{2a}$

 

  from ΔAFD

${\mathrm{c}}^2={\mathrm{a}}^2+{\mathrm{b}}^2$

${\mathrm{c}}^2={\mathrm{a}}^2+2{\mathrm{a}}^2$

${\mathrm{c}}^2=3{\mathrm{a}}^2$

$\mathrm{c}=\sqrt{3\mathrm{a}}$

 

Let the radius of the atom be r.

Length of the body diagonal

$c= 4\pi$

$\sqrt{3a}=4r$

$\mathrm{a}=\frac{4\mathrm{r}}{\sqrt{3}}$

$\mathrm{r}=\frac{\sqrt{3\mathrm{a}}}{4}$

$a^3={\left(\frac{4r}{\sqrt{3}}\right)}^3$

 

A body-centred cubic lattice contains 2 atoms.

So, volume of the occupied cubic lattice

$=2\mathrm{\pi }\frac{4}{3}{\mathrm{r}}^3$

$=\frac{8}{3}{\mathrm{\pi r}}^3$

Packing efficiency $\frac{\mathrm{Volume} \mathrm{occupied} \mathrm{by} \mathrm{two} \mathrm{spheres} \mathrm{in} \mathrm{the} \mathrm{unit} \mathrm{cell}}{\mathrm{Total} \mathrm{volume} \mathrm{of} \mathrm{the} \mathrm{unit} \mathrm{cell}}\times 100\%$

$=\frac{{\displaystyle \frac{8}{3}}{\mathrm{\pi r}}^3}{{\left({\displaystyle \frac{4}{\sqrt{3}}}\mathrm{r}\right)}^3}\times 100\%$

$=\frac{{\displaystyle \frac{8}{3}}{\mathrm{\pi r}}^3}{{\left({\displaystyle \frac{64}{\sqrt[3]{3}}}{\mathrm{r}}^3\right)}^{}}\times 100\%$

 

= 68%

 

(iii) Face-centred cubic

Let the edge length of the unit cell be ‘a’ and the length of the face diagonal AC be b.

From ΔABC

$A{C}^2=B{C}^2+A{B}^2$

$b^2=a^2+a^2$

$b^2=2a^2$

$\mathrm{b}=\sqrt{2\mathrm{a}}$

 

Let r be the radius of the atom.

from the figure, it can be observed that

$\mathrm{b}=4\mathrm{r}$

$\sqrt{2\mathrm{a}}=4r$

$\mathrm{a}=2\sqrt{2\mathrm{r}}$

Volume of the cube

$a3={\left(\sqrt[2]{2r}\right)}^3$

We know that the number of atoms per unit cell is 4.

Volume of the occupied unit cell

$=4\pi \frac{4}{3}{r}^3$

Packing efficiency = $\frac{Volume occupied by four spheres in the unit cell}{Total volume of the unit cell}\times 100\%$

$=\frac{4\pi \frac{4}{3}{r}^3}{{\left(\sqrt[2]{2r}\right)}^3}\times 100\%$

$=\frac{\frac{16}{3}\mathrm{\pi }{r}^3}{\sqrt[16]{2r^3}}\times 100\%$

=74%

 

 

 

Question 1.7) How will you distinguish between the following pairs of terms

 

Question 1.7) How will you distinguish between the following pairs of terms:

(i) Hexagonal close-packing and cubic close-packing?

(ii) Crystal lattice and unit cell?

(iii) Tetrahedral void and octahedral void?

Answer :

(a) Cubic close packing:-

When a third layer is placed over the second layer in a manner that the octahedral voids are covered by the spheres, a layer different from the first

(A) and second

(B) is obtained.

If we continue packing in this manner we get the cubic close packing.Hexagonal close packing: When the third layer is placed over the second layer in a way that the tetrahedral voids are covered by the spheres, a 3D close packing is produced where spheres in each third or alternate layers are vertically aligned. If we continue packing in this order we get hexagonal close packing.

(b) Unit cell:-

It is the smallest 3D dimensional portion of a complete space lattice, which when repeated over and over again in different directions from the crystal lattice.

Crystal lattice :-

it is a regular orientation of particles of a crystal in a 3D space.

(c) Octahedral void :-

it is a void surrounded by 6 spheres.

Tetrahedral void :-

it is a void surrounded by 4 spheres.

 

 

 

 

 

 

 

 

 

Master of Technology (M. Tech.) in Mechanical Engineering, abhilashiuniversity.com/

 Master of Technology (M. Tech.) in Mechanical Engineering.

Seats:

15 
Course Duration: 2 Years (4 Semesters)

Eligibility and Admission Criteria for Postgraduate Programs:

The candidate should have passed B. Tech. examination in the respective branch of engineering with minimum entry level qualification prescribed by AICTE.

Admission:

Admission will be made on the basis of merit of GATE/Entrance Examination or 60% marks for general category (55% marks for SC/ST category) in the qualifying examination conducted by the recognized University.

 

 

Master of Technology (M. Tech.) in Civil Engineering

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Eligibility and Admission Criteria for Postgraduate Programs:

The candidate should have passed B. Tech. examination in the respective branch of engineering with minimum entry level qualification prescribed by AICTE.

Admission:

Admission will be made on the basis of merit of GATE/Entrance Examination or 60% marks for general category (55% marks for SC/ST category) in the qualifying examination conducted by the recognized University.

 

 

Master of Technology (M. Tech.) in Computer Science Engineering

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The candidate should have passed B. Tech. examination in the respective branch of engineering with minimum entry level qualification prescribed by AICTE.

Admission:

Admission will be made on the basis of merit of GATE/Entrance Examination or 60% marks for general category (55% marks for SC/ST category) in the qualifying examination conducted by the recognized University.

 

M.SC (Agronomy)
Course : M.Sc. Agriculture (Agronomy)
Seats :  06
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Eligibility: B.Sc. (Hons.) Agriculture/ Horticulture/ Forestry/ Sericulture/B.Sc. Agriculture/Horticulture/Forestry Sericulture (4/5/6years programmers only)with minimum 50% marks.

Admission: Admission will be made on the basisof merit of entrance examination conducted by AbhilashiUniversity (AUCET-2020)or  CSKHPKV Palampur or Dr.Y.S. Parmar UHFNauni (Solan).

 

 

 

 

 

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Duration: 02 years

Seat:40

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A candidate who has passed bachelor's degree in any stream from a recognized University with 50% marks (45% for SC/ST). In addition, 10% weightage on the marks obtained in B.Ed Examination will be given to the candidate possessing B.Ed. degree from recognized university.

Admission: Merit in the AUCET and as per the marks in qualifying examinations.

Master in Pharmacy (Pharmaceutics, Pharmaceutical Chemistry and Pharmacology)

Duration: 2 years (4 semesters)

Seats: Pharmaceutics 06, Pharmaceutical Chemistry 09, Pharmacology 12

Eligibility: 

The admission to M Pharmacy degree course shall be made on the basis of merit of valid GPAT score. In case the seats remain vacant after exhausting the merit of GPAT, the vacant seats will be filled up on the basis of merit of HPCET. In case the seats still remain vacant after exhausting the merit of National level test and HPCET, the seats will be filled up on the basis of merit of B. Pharmacy degree awarded by the recognized University having minimum 55% for Gen and 50% for (SC/ST).

M.Sc. Zoology

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Admission: Merit in the AUCET

 

M.Pharmacy (Pharmaceutical Chemistry)

Duration:  2 years (4 semesters).

Seats:   Pharmaceutics 06, Pharmaceutical Chemistry 09, Pharmacognosy 15

Eligibility:  The admission to M Pharmacy degree course shall be made on the basis of merit of valid GPAT score. In case the seats remain vacant after exhausting the merit of GPAT, the vacant seats will be filled up on the basis of merit of HPCET. In case the seats still remain vacant after exhausting the merit of National level test and HPCET, the seats will be filled up on the basis of merit of B. Pharmacy degree awarded by the recognized University having minimum 55% for Gen and 50% for (SC/ST).

 

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Seats:              Pharmaceutical Sciences 06 

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Duration:  3 years (6 semesters)

 

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The candidate must have passed MBA/M.Com. Examination from a recognized University with 55% marks for general category (50% marks for SC/ST category).

Master of Business Administration (MBA)

 

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Seats:40

 

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Duration: 2 Years

Seats: 60

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Admission: The admission will be made on the basis of marks in the qualifying examination.

B.Sc. (Hons.) Agriculture

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Seats: 120

Eligibility:

Candidates having passed 10+2 with science and secured not less than 60% marks in aggregate for general category and 55% for SC/ST who have qualified AUCET-2018. Candidates securing 50% marks in aggregate for general category (40% for SC/ST) who have appeared in state level entrance test conducted by CSKHPKV, Palampur or Dr. Y.S. Parmar University of Horticulture and Forestry, Nauni (Solan). 

 

Admission:

The admission will be made on the basis of marks in entrance examination conducted by Abhilashi University (AUCET-2018) or CSHKPKVV,Palampur or Dr. Y.S. Parmar UHF, Nauni (Solan).

Bachelor of Ayurvedic Medicine and Surgery, B.A.M.S.

 

Abhilashi Ayurvedic College andResearch Institute is running Bachelor of Ayurvedic Medicine and Surgery (BAMS) programme on the annual system of teaching and evaluation.

 

 

Duration:

 

Five and half years including Compulsory Rotatory internship of one year.

 

Seats: 60

 

Eligibility & Admission Criteria:

 

Admissionin BAMS Course will be done on the basis of merit in NEET and qualifying examination with minimum 50% in 10+2 (Medical)with valid NEET score 05%relaxation for SC/ST.

 

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Lateral Entry:

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D.Pharma (Ayurveda)

Diploma in Pharmacy (Ayurveda):

Duration: 2 Years.

 

Seat: 60

 

Eligibility: 

 

A candidate who has passed 10+2.

 

Admission:

 

The admission will be made on the basis of marks in the qualifying examination.

D.Pharma ( Allopathy)

Diploma in Pharmacy (Allopathy) (D. Pharmacy)

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Seats: 60

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B.A. B.Ed. & B.Sc. B.Ed

Department of Education and Science.

School of Education, Abhilashi University ensures to provide the better quality teaching fraternity to the State and the Nation. As a teacher is considered to be builder of the nation so in this tune role of good teacher becomes of paramount importance. Abhilashi University offers various courses viz. M.A. Education, Ph.D. Education. The Department of Education Intends to start B.A. B.Ed. & B.Sc.B.Ed., 4 yrs Integrated Teacher education Programme (Pre-Primary to Primary /Upper Primary to Secondary).