# Optionals IAS Mains Physics: Questions 223 - 228 of 307

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## Question 223

Appeared in Year: *2005*

### Describe in Detail

Essay▾Draw the logic circuit for the following Boolean expression:

What are the values for the input combinations:

- 1,1, 0
- 1,0, 1
- 0,0, 1

### Explanation

1 | 1 | 0 | 1 | 0 | 1 | 1 |

1 | 0 | 1 | 1 | 0 | 0 | 0 |

0 | 0 | 1 | 0 | 1 | 0 | 1 |

## Question 224

Appeared in Year: *2005*

### Describe in Detail

Essay▾Determine the reciprocal lattice vector of an FCC lattice.

### Explanation

The primitive translation of an FCC lattice, as shown in fig 1 are

Volume of the primitive cell is given by

The primitive translation vector of the reciprocal lattice is obtained as

Similarly,

The primitive translation vector of a BCC lattice is given by

If we compare in equation (1) with equation (2) we find that these equations are simila…

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## Question 225

Appeared in Year: *2018*

### Describe in Detail

Essay▾Show that for free electron gas, the density of states in three dimensions (3D) varies as , and this dependence changes to for 2D (quantum well) , for 1D (quantum write) and function for OD (quantum dot) . (Paper-II)

### Explanation

For an electron in one-dimensional metal (i.e.. an electron in a one-dimensional potential box with periodic boundary conditions) , the energy Eigen values are given by

with

In figure we plot the relation (a) and show the allowed values of energy E and wave vector k. Let us choose two points K and . Let the cores pending energies be E and . 2f the …

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## Question 226

Appeared in Year: *2005*

### Describe in Detail

Essay▾Show that the length of an object moving with a velocity is given by

Where is the proper length and is the velocity of light in free space.

What will be the shape of a spherical ball while moving under relativistic regime?

### Explanation

The length of a rod, as measured in a frame of reference, at rest with respect to the observer, is called its proper length and would obviously be the same in all stationary frame of reference. It is only in moving frames that at will be different, depending upon their relative velocities with respect to the observer. Let us see how.

Consider a rod …

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## Question 227

Appeared in Year: *2010*

### Describe in Detail

Essay▾What is spin-orbit interaction? Calculate the energy shift due to spin orbit interaction term in like system. Discuss the significance of this term (shift) in relation to the fine structure of hydrogen spectral lines.

### Explanation

The spin orbit interaction is an interaction between an electron՚s spin magnetic dipole moment and the internal magnetic field of an atom which arises from the orbital motion of the electron through the nuclear electric field. Since the internal magnetic field is related to the electron՚s orbital angular momentum, this is called the spin-orbit inte…

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## Question 228

Appeared in Year: *2005*

### Describe in Detail

Essay▾Describe Stern Gerlach experiment and discuss its implications.

### Explanation

In this, first sliver (Ag) atoms are heated in an oven. The oven has a small hole through which some of the silver atoms escape. As shown in fig (1) , the beam goes through a collimator and is then subjected to an on homogeneous magnetic field produced by a pair of pole pieces, one of which has a very sharp edge.

We must now work out the effect of m…

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