# Optionals IAS Mains Physics: Questions 172 - 177 of 307

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## Question 172

Appeared in Year: *2010*

### Describe in Detail

Essay▾Show that the Pauli spin matrices satisfy the following:

### Explanation

(Identity matrix)

## Question 173

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*

### Describe in Detail

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*

### Describe in Detail

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*

### Describe in Detail

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*

### Describe in Detail

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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