The distance between the adjacent atomic planes in CaCO3 is 0.3 nm. The smallest angle of Bragg scattering for 0.03 nm X-ray is

If $$\sigma $$ is the total cross-section and f(θ), θ being the angle of scattering, is the scattering amplitude for a quantum mechanical elastic scattering by a spherically symmetric potential, then which of the following is true? Note that k is the magnitude of the wave vector along the $${{\bf{\hat z}}}$$ direction.

A

$$\sigma = {\left| {f\left( \theta \right)} \right|^2}$$

B

$$\sigma = \frac{{4\pi }}{k}{\left| {f\left( {\theta = 0} \right)} \right|^2}$$

C

$$\sigma = \frac{{4\pi }}{k} \times {\text{Imaginary part of }}{\left| {f\left( {\theta = 0} \right)} \right|^2}$$

D

$$\sigma = \frac{{4\pi }}{k}{\left| {f\left( \theta \right)} \right|^2}$$

For a NaCI crystal, the cell-edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are

A

1 0 0

B

1 1 0

C

1 1 1

D

2 0 0

The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?

A

80 degrees

B

60 degrees

C

120 degrees

D

40 degrees

Consider the following statements
1. The sky appears blue because of scattering.
2. The main cause of seven colors of the rainbow is scattering of light.
3. At the time of sunrise, the sun appears red, due to scattering of light.
Choose the correct statement/s from the given options

A

Only 1 is true

B

1 and 3 is true

C

Only 2 is true

D

2 and 3 is true

In a cubic crystal, atoms of mass M₁ lie on one set of planes and atoms of mass M₂ lie on planes interleaved between those of the first set. If C is the forte constant between nearest neighbour planes, the frequency of lattice vibrations for the optical phonon branch with wave vector k = 0 is

A

$$\sqrt {2C\left( {\frac{1}{{{M_1}}} + \frac{1}{{{M_2}}}} \right)} $$

B

$$\sqrt {C\left( {\frac{1}{{2{M_1}}} + \frac{1}{{{M_2}}}} \right)} $$

C

$$\sqrt {C\left( {\frac{1}{{{M_1}}} + \frac{1}{{2{M_2}}}} \right)} $$

D

zero

Which of the following statements is/are false regarding modern periodic table?
1. Elements in the modern periodic table are arranged in decreasing order of their atomic numbers.
2. Elements in the modern periodic table are arranged in increasing order of their atomic masses.
3. In the modern periodic table, isotopes are placed in adjacent groups.
4. Elements in modern periodic table are arranged in increasing order of their atomic numbers.

A

only 1

B

only 4

C

1, 2 and 4

D

1, 2 and 3

An object is kept in one of the quadrants of principal planes of projection, for both the front view and top view of the object the object came first and then the views on planes (the observer is at top right side of principal planes). The object is in which quadrant?

A

1st quadrant

B

2nd quadrant

C

3rd quadrant

D

4th quadrant

Before a battle the ratio of tanks to planes in an army was 5 : 3. During the war 1000 tanks were destroyed and 800 planes were destroyed. The ratio oftanks to planes became 2 : 1. What is the number of tanks after the war.

A

2000

B

1000

C

3000

D

4000

The scattering of waves in Bragg’s law experiment is due to __________

A

Einstein’s scattering

B

Rayleigh scattering

C

Newton scattering

D

Inelastic scattering

X-ray crystallography are
P. Based on the elastic scattering of X-rays
Q. Non-destructive analytical techniques
R. Used in determining the arrangement of atoms within a crystal
S. Based on Bragg's law

A

P and Q

B

R and S

C

P, Q and S

D

All of the above

The distance between the adjacent atomic planes in CaCO₃ is 0.3 nm. The smallest angle of Bragg scattering for 0.03 nm X-ray is

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