# Optionals IAS Mains Physics: Questions 299 - 305 of 306

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## Question 299

Appeared in Year: *2006*

### Describe in Detail

Essay▾Drawing necessary diagrams, explain diamond structure and structures. (Marks: 10)

### Explanation

Diamond structure: The diamond lattice (formed by the carbon atoms in a diamond crystal) consists of two interpenetrating face – centred cubic Bravais lattices, displaced along the body diagonal of the cubic cell one quarter the length of the diagonal. It can be regarded as a face – centred cubic lattice with the two – point basis and. The coordin

… (230 more words) …

## Question 300

Appeared in Year: *2015*

### Write in Short

Short Answer▾Find the magnetic moment of an atom in state, assuming that coupling holds for this case. (Marks: 10)

## Question 301

Appeared in Year: *2003*

### Write in Short

Short Answer▾A particle of mass m, with energy E such that, is trapped in a potential well as shown below: (Marks: 15)

Obtain an expression from which the energy Eigen values can be determined. (Marks: 15)

## Question 302

### Describe in Detail

Essay▾**Two long coaxial cylindrical metal tubes (inner radius a, outer radius b) stand vertically in a tank of dielectric oil (susceptibility, mass density ρ). Inner one is maintained at potential V and outer one is grounded. To what height (h) does oil rise, in space between tube?**

### Explanation

Coaxial cylinder with air part:

Let be the charge density (i. e. , charge per unit length)

For air part of tube

Electric field in this case is:

E= ()

But E= (V = potential maintained)

So

- =

=- (at r = a; potential is V and at r = b potential is zero)

In FOR AIR PART OF COAXIAL TUBE ……. . 1

Coaxial cylinder with oil part:

Let λ2 be the charge density (i.

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## Question 303

### Describe in Detail

Essay▾**Consider a particle of mass mxx moving freely between =0 and =a inside an infinite square well potential.**

**(a) Calculate the expectation values, , and .**

### Explanation

Since **=** **sin** ( and it is a real function

For expectation value of momentum

= expectation value of momentum (P)

= =

=

= 0 ()

For expectation value of X

= expectation value of X

= =

= ()

= [

= - 0

=

For expectation value of

= expectation value of

= =

= ()

= [

= +

= 0 { [ } }

= { -0}

=

For expectation value of

= expectation value of P^{2}

= =

## Question 304

### Explanation

- When the theory of relativity appeared in the early 1900s, it upended centuries of science and gave physicists a new understanding of space and time.
- Isaac Newton saw space and time as fixed, but in the new picture provided by special relativity and general relativity they were fluid and malleable.

*Who came up with theory of relativity?*

**Albert Einstei**

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## Question 305

### Describe in Detail

Essay▾**Consider a particle of mass mxx moving freely between =0 and =a inside an infinite square well potential.**

**Calculate uncertainties product **

### Explanation

The position and momentum uncertainties can be calculated

**=** **=** **=**

**=** **=** **=**

=