Optionals IAS Mains Physics: Questions 53 - 59 of 307

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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

Wave Equations in Vacuum, Poynting Theorem, Vector and Scalar Potentials
Edit

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.…

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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)

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Question 56

Edit

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…

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Question 58

Classification of Elementary Particles and Their Interactions
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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…

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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…

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