Optionals IAS Mains Physics: Questions 299 - 305 of 306

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Question 299

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Appeared in Year: 2006

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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

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Question 300

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Appeared in Year: 2015

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Short Answer▾

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

Question 301

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Appeared in Year: 2003

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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

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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

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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 P2

= =

Question 304

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Essay▾

Write a short note on Theory of Relativity.

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

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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

= = =

= = =

=