# Optionals IAS Mains Physics: Questions 112 - 118 of 307

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## Question 112

Appeared in Year: *2012*

### Describe in Detail

Essay▾The Einstein theory of specific heat of solids gives the expression

Where with as the Einstein temperature.

(ii) Give schematic plot of V/S and common on the validity of expressions in (i) in comparison with experiments.

### Explanation

- A theoretical plot of V/S using given equation for diamond using is shown below. Some experimental points are also shown for comparison. It is seen that the Einstein curve fits the experimental points well over a wide range of temperature except for very low (liquid helium) temperatures where it falls more rapidly than the observed decrease in …

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## Question 113

### Explanation

- The Boolean equation for is .

- The Boolean equation for is .

The first equation describes a NOR gate, and the second equation a bubbled AND gate. Since the outputs are equal for the same inputs, we can equate the right-hand members to get

The identity is known as De Morgan՚s first theorem. In words, it says the complement of a sum equ…

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## Question 114

Appeared in Year: *2016*

### Describe in Detail

Essay▾Show that the Young՚s modulus , modulus of rigidity and Poisson՚s ratio are related by the equation .

### Explanation

Let the upper face ABEG of a cube of each edge be sheared through an angle under a tangential force applied to it, as shown in Fig (1) , such that displacement AA ‘= BB’ = , with diagonal DB increased to DB ‘and diagonal AC shortened to A’ C. Then clearly, tangential stress applied , say and shear strain produced . Therefore the modulus of rigid…

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## Question 115

Appeared in Year: *2004*

### Describe in Detail

Essay▾What are the term symbols for atoms with the following (total spin) and (total orbital) quantum numbers, ?

### Explanation

The term symbols are denoted by

Since ,

Corresponds to state

Lies between to

to

,

Term symbols are and

## Question 116

Appeared in Year: *2004*

### Describe in Detail

Essay▾A point charge is held at a distance in front of an infinite grounded conducting plane. What is the electric potential in front of the plane?

### Explanation

We suppose that the conducting plane is specified at and the point charge is located at If we imagine a point charge at it is the required image charge for the problem. This is because when we have a pair of equal and opposite point charges, the surface perpendicular to the line joining them and midway between them is a zero potential surface …

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## Question 117

Appeared in Year: *2004*

### Describe in Detail

Essay▾A hydrogen atom is in the following state: .

What is the probability of finding the system in the state ?

### Explanation

Using the orthonormality condition, where we can verify that is normalized.

Since is normalized, the probability of finding system in is given by

Since and

## Question 118

Appeared in Year: *2004*

### Describe in Detail

Essay▾By drawing v/s curve, distinguish between metal, insulator and semiconductor.

### Explanation

To distinguish between metals, insulators and semiconductors on the basis of the band theory, we consider an energy band which is filled with electrons up to a certain value. as shown in Fig (1) .

It is of interest to know the effective number of free electrons present in this band gives information about the conductivity of the band.

In the express…

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