Optionals IAS Mains Physics: Questions 172 - 177 of 307

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Question 172

The Spin Half Problem and Properties of Pauli Spin Matrices

Appeared in Year: 2010

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Essay▾

Show that the Pauli spin matrices satisfy the following:

Explanation

(Identity matrix)

Question 173

Edit

Appeared in Year: 2010

Describe in Detail

Essay▾

Obtain Poisson՚s equation in electrostatics from Gauss՚ law. What form does it take when the charge density is zero?

Explanation

Poisson՚s and Laplace՚s equations are easily derived from gauss՚s law (for a linear, isotropic material medium)

And

Substituting (2) in (1) gives

For an inhomogeneous medium. For a homogeneous medium, equation (3) becomes

This is known as Poisson՚s equation. A special case of this equation occurs when = (i.e.. for a charge free region) . Equation (4…

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Question 174

Appeared in Year: 2010

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Essay▾

If a photon of frequency collides with on electron of rest mass , it will be scattered at some angle with a new frequency show that the change in wavelength is related to the scattering angel by the formula Where is known as the Compton wavelength.

Explanation

  • The Compton Effect experiment gives direct evidence that electromagnetic radiations consist of photons, which collide with electrons, for example, like one billiard ball colliding with other ball. In fig (1) , we show schematically, the experimental arrangement of Compton Effect. An X-ray beam of known single wavelength from source S falls on the m…

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Question 175

Appeared in Year: 2010

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Essay▾

Is it possible to obtain pure rotational spectra of and molecules?

Explanation

  • Molecules that have permanent electric dipole moments can absorb or emit electromagnetic radiation in for infra-red or microwave transition. It means that homonnuclear diatomic molecules such as symmetric linear molecules such as and spherical-top polyatomic molecules such as do not exhibit rotational spectra.
  • In practice, rotational spectra are …

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Question 176

Appeared in Year: 2010

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Essay▾

Explain the reduced zone scheme of plotting the energy bands in solids. On the basis of V/S curve, distinguish between conductors, semiconductors and insulators.

Explanation

When we solve the determinate from the kroning penny model, we get

To simplify this equation, Kronig and Penny considered the case when and b approaches zero but the product remains finite, i.e.. the potential barriers become delta function. Under these circumstances, the model is modified to the one of a series of wells separated by initially thi…

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Question 177

Appeared in Year: 2010

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Essay▾

Discuss occurrence of rotational energy levels of a diatomic molecule and show that the pure rotation spectrum of such a molecule consists of a series of equally spaced lines separated by a constant wave number difference . write down the selection rules.

Explanation

  • As we know, all (heteronuclear) diatomic molecules with “unlike” atoms, for which the Centers of positive and negative charges do not coincide, have a permanent dipole moment. During the rotation of the molecule, the component of the dipole moment in a fixed direction changes periodically with the frequency of rotation, , of the molecule so that, …

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