# Optionals IAS Mains Physics: Questions 211 - 216 of 307

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## Question 211

Appeared in Year: *2005*

### Describe in Detail

Essay▾Set up the time independent Schrodinger equation for an electron moving in coulomb field, in polar coordinates. Solve the radial equation to get the energy Eigen values.

### Explanation

Let us express the Hamiltonian operator in polar coordinates as

Where is expressed as

The orbital angular momentum operator is given by

Therefore may be written as

So the three – dimensional, time independent Schrodinger equation of a article in a potential may be written as

Or

The orbital angular momentum operators and don՚t contain the radial v…

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## Question 212

Appeared in Year: *2005*

### Describe in Detail

Essay▾What is the essential difference between interference and diffraction of light? How can you achieve Fraunhofer diffraction in the laboratory? Using the concept of Fraunhofer diffraction at a single slit, find out the intensity distribution produced by two slit of equal width.

### Explanation

The main differences between interference and diffraction are as follows:

Interference | Diffraction |

(1) Interference is the result of interaction of light coming from different wave fronts. | (1) Diffraction is the result of interaction of light coming from different parts of the same wave front. |

(2) Interference fringes may or may not be of the same width. | (2) Diffraction fringes are not of the same width. |

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## Question 213

Appeared in Year: *2018*

### Describe in Detail

Essay▾Prove the following identities: - (Paper-II)

### Explanation

We know that angular momentum component operator is expressed as where I, j, k are in cycle order (i, j, k = 1,2, 3) .

Let us take commutator in cyclic order

We have

Question: 8. Prove the following identities: -

Writing the expansion of

If

if is along x and if is along y.

Let us consider has 2 components i.e.. along x and y.

If is considered …

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## Question 214

Appeared in Year: *2005*

### Describe in Detail

Essay▾Discuss briefly the concept of effective mass in semiconductors and explain the significance of negative effective mass.

### Explanation

The effective mass is defined as

The indicates that the effective mass of an electron isn՚t constant but depends on the values of . i.e.. on the shape of the curve. The variation of effective mass with k is shown in fig (1) . The effective mass is positive in the lower half of the energy band and negative in the upper half. Thus the electron behav…

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## Question 215

Appeared in Year: *2018*

### Describe in Detail

Essay▾Derive an expression for lattice specific heat in Debye model. Find its low temperature limit (Debye ) (Paper -II)

### Explanation

If the inter atomic distance is small as compared to the wavelength of elastic waves, the crystal can be regarded as a continuum from the point of view of the wave. Based on this idea, Debye assumed that the continuum model is applicable to all possible vibrational modes of the crystal. Further the fact that the crystal consists of a finite no. (N)…

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## Question 216

Appeared in Year: *2005*

### Describe in Detail

Essay▾Calculate the De – Broglie wavelength of an electron moving with a kinetic energy of

### Explanation

Let the electron of rest mass and electric charge be accelerated from rest by a potential to velocity , then,

Its wavelength