# Optionals IAS Mains Physics: Questions 93 - 99 of 306

Access detailed explanations (illustrated with images and videos) to **306** questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. *Unlimited Access, Unlimited Time, on Unlimited Devices*!

View Sample Explanation or View Features.

Rs. 750.00 -OR-

How to register? Already Subscribed?

## Question 93

## Question 94

## Question 95

Appeared in Year: *2009*

### Describe in Detail

Essay▾The quantum mechanical probability distribution function of an electron of ground state of hydrogen atom is

Using the result deduct that N is proportional to. (20 Marks)

### Explanation

Applying integration by parts on the above integral

It is clear that exponential will “beat” any power function as of tends to.

Hence N is proportional to.

… (2 more words) …

## Question 96

Appeared in Year: *2009*

### Describe in Detail

Essay▾Using Planck’s radiation formula, deduce Wein’s displacement law. (10 Marks)

### Explanation

- Planck’s formula is given by
- Differentiating it partially with respect to, we get
- For maximum value of emission, i. e. for maximum value of must be equal to zero i.e..
- Putting, the above expression becomes
- It is obvious from this equation that there must be a root in the neighbourhood of 5. Applying the method of approximation the exact value

… (32 more words) …

## Question 97

Appeared in Year: *1999*

### Describe in Detail

Essay▾For a particle confined in a one dimensional potential well of length L the wave function is

And outside

Calculate the expectation values of. (20 Marks)

### Explanation

Formula used:

Here we have applied formula of integration by parts

I. e.

Denominator: (calculated previously)

Numerator:

Divided and multiplied by 2 and

## Question 98

Appeared in Year: *2013*

### Describe in Detail

Essay▾If the forces acting on a particle are conservative, show that the total energy of the particle which is the sum of the kinetic and potential energies is conserved.

### Explanation

If the particle is acted upon by the forces which are conservation, that is, if the forces are derivable form a scalar potential energy function in the manner then the total energy of the particle (Kinetic + Potential) is conserved.

Suppose, under the action of such a force, a particle moves form particle will be

If the particle moves distance in

… (43 more words) …

## Question 99

Appeared in Year: *2013*

### Describe in Detail

Essay▾Show that a particle of rest mass and total energy E and linear momentum satisfies the relation Where c is the velocity of light in free space.

### Explanation

A simple relation between relativistic momentum (and relativistic energy (E) of a particle of rest mass is easily obtained from the expressions for and . For, clearly , so that

Which enables us to determine the velocity of the particle from the values of its momentum and energy since, clearly,

Another important relation between and E may be obt

… (73 more words) …