# Optionals IAS Mains Physics: Questions 47 - 52 of 306

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## Question 47

### Write in Short

Short Answer▾Prove that the value of is nearly Hence determine the Fermi temperature of a metal whose Fermi energy is.

## Question 48

Appeared in Year: *2011*

### Describe in Detail

Essay▾What led Vander Waals to modify the ideal gas equation? Using the concepts of critical temperature, pressure and volume, show that the critical constant for a real gas is (20 marks)

### Explanation

- The ideal gas equation is given by Where is the number of moles or equivalently by
- Where is the molar volume (i.e. the volume occupied by 1 mole).
- This equation of state leads to isotherms. However, real gas don’t behave quite like this, particularly when the pressure is high and the volume is small. If you get a real gas cold enough it will liqu

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## Question 49

Appeared in Year: *2007*

### Describe in Detail

Essay▾Solve the Schrodinger equation for a linear harmonic oscillator obtain the eigen values and the corresponding Eigen functions. (40 Marks)

### Explanation

- The Schrodinger equation for harmonic oscillator is ……………. eq. (1)
- And solve it directly by the series method. Let us introduce a dimensionless variable …………eq. (2)
- In terms of, the Schrodinger equation reads …………. . eq. (3)
- Where k is the energy, in units of …………eq. (4)
- Our problem is to solve equation (3) and in the process obtain the “allowed” v

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## Question 50

Appeared in Year: *2003*

### Describe in Detail

Essay▾What is a Josephson junction? Discuss Josephson Effect and obtain the relation

Or frequency (30 Marks)

### Explanation

- A Josephson junction is made by sandwilling a thin layer of a non-superconducting material between two layers of superconducting material. The devices are named after Brian Josephson, who predicted in 1962 that pairs of the superconducting electrons could “tunnel” right through the non-superconducting barrier from one superconductor to another. He

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## Question 51

Appeared in Year: *2002*

### Describe in Detail

Essay▾The phase velocity of the surface wave in a liquid of surface tension T and density is given by

Show that the group velocity of the surface wave is given by (20 marks)

### Explanation

As

As is given to be

Multiply numerator and denominator by

Hence proved

## Question 52

Appeared in Year: *2003*

### Describe in Detail

Essay▾Express the Cartesian components of the angular momentum L in operator form. Show that. What is the significance of this commutation relation? (15 Marks)

### Explanation

The orbital angular momentum can be obtained at once by replacing by the corresponding operators in the position representation,

The Cartesian components of are

Clearly, angular momentum doesn’t exist in a one dimensional space.

The importance of this observable is that it is compatible with any of the Cartesian components of the angular momentum

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