# Optionals IAS Mains Physics: Questions 53 - 59 of 307

Access detailed explanations (illustrated with images and videos) to **307** 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 53

Appeared in Year: *2002*

### Describe in Detail

Essay▾The wave function of the particle is

Find the expectation value of position (x) and momentum (p) of the particle.

(10 marks)

### Explanation

As is a odd function.

Numerator

(Odd function)

Denominator

## Question 54

Appeared in Year: *2015*

### Describe in Detail

Essay▾Derive the equation that represents Poynting՚s theorem. What is its physical significance? (20 Marks)

### Explanation

- We know that
Electromagnetic potential energy … eq. (1)

Energy stored in a magnetic field … eq. (2)

- Maxwell՚s equations in differential form are
Or … eq. (3)

Or … eq. (4)

Or … eq. (5)

Or … eq. (6)

- Taking scalar product of equation (5) with H and equation (6) with E, we get
… eq. (7)

… eq. (8)

- Subtracting equation (8) from equation (7) we get
… eq.…

… (556 more words) …

## Question 55

Appeared in Year: *1999*

### Describe in Detail

Essay▾Find the Broglie waves length associated with an electron of energy (20 Marks)

### Explanation

Where h is the Planck՚s constant and p is the momentum.

So

Or the direct method is

(ii)

… (2 more words) …

## Question 56

Appeared in Year: *2002*

### Describe in Detail

Essay▾A 200 eV increase in the energy of an electron changes its De Broglie wavelength by a factor of 2. Calculate the initial De Broglie wavelength of the election. (20 marks)

### Explanation

(Here V is in volts)

As we can see from this relation that is inversely proportional to the square of E so increase in energy will decrease the wavelength.

So,

## Question 57

Appeared in Year: *2015*

### Describe in Detail

Essay▾Show that the differential scattering cross section can be expressed as

Where s is the impact parameter and is the scattering angle. (15 Marks)

### Explanation

- Let us consider a uniform beam of particles all of the same mass and kinetic energy, incident upon the centre of force. The incident beam is characterized by specifying its intensity I, defined as the number of particles crossing unit area normal to the beam in unit time.
- When the experiment is performed with many particles simultaneously, then inst…

… (232 more words) …

## Question 58

Appeared in Year: *2002*

### Describe in Detail

Essay▾Distinguish between Hadrons and leptons. (10 Marks)

### Explanation

- Elementary particles fall into two classes, leptons and hadrons, depending on whether they respond to the strong interaction (hadrons) or do not (leptons) .
- The simplest particles are the leptons, which seen to be truly elementary with no hint of internal structures or ever of extension in space. Leptons are effected by the electromagnetic (if charg…

… (463 more words) …

## Question 59

Appeared in Year: *2002*

### Describe in Detail

Essay▾Show that the potential energy of a charge Q uniformly distributed throughout the sphere of radius R is given by (20 marks)

### Explanation

- Let as assume that the sphere has Radius R and ultimately will contain a total charge Q uniformly distributed throughout its volume. The electrostatic potential energy U is equal to the work done in assembling the total charge Q within the volume i.e. the work done in bringing Q from infinity to the sphere. We can do this by bringing a series of ve…

… (199 more words) …