# Optionals IAS Mains Physics: Questions 162 - 166 of 306

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## Question 162

Appeared in Year: *2016*

### Describe in Detail

Essay▾Using uncertainty principle, calculate the size and energy of the ground state of hydrogen atom.

### Explanation

According to the uncertainty principle, the electron’s momentum and the radius of the its orbit related by ; hence . To find the ground state radius, we simply need to minimize the electron – proton energy

With respect to

This leads to the Bohr radius

Inserting into , we obtain the Bohr energy:

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## Question 163

Appeared in Year: *2007*

### Describe in Detail

Essay▾What are chromatic and spherical aberrations. Explain. Calculate the longitudinal aberration for rays at a height of from the principle axis and incident on the cowed surface (radius of curvature=) of a thin piano – convex lens made of glass (refractive index = 1.5**)**

### Explanation

- Aberrations are divided broadly into two categories – monochromatic aberrations and chromatic aberrations. The defects due to wide – angle incidence and peripheral incidence, which occur even with monochromatic light, are called monochromatic aberrations. Aberration that occur due to dispersion of light are called chromatic aberration. Chromatic ab

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## Question 164

Appeared in Year: *2007*

### Describe in Detail

Essay▾Define resolving power and dispersive power of a grating. Two spectral lines of wavelength and are seen clearly resolved in the second order spectral of a grating. If the grating has line per cm, what should be the minimum width of the grating?

### Explanation

- Dispersive power of a grating: It is defined as the radio of the radio of the difference in the angle of diffraction of any two neighboring spectral lines to the difference in wavelength between the two spectral lines. It can also be defined as the difference in the angle of diffraction per unit change in wavelength. The diffraction of the order p

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## Question 165

Appeared in Year: *2016*

### Describe in Detail

Essay▾The primitive translation vectors of a two – dimensional lattice are,

Describe the primitive translation vectors of its reciprocal lattice.

### Explanation

We assume that the third translation vector of the given lattice lies along the – axis and is of unit magnitude i. e.

The reciprocal lattice vectors are given by

,

It is obvious that vectors and lie in the plane of and

and are the required reciprocal vectors.

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## Question 166

Appeared in Year: *2007*

### Describe in Detail

Essay▾What is Josephson Effect? Discuses briefly DC and AC Josephson Effects. Give some practical application of Josephson junctions.

### Explanation

- Josephson observed some remarkable effects associated with the tunneling of superconducting electrons through a very thin insulator sandwiched between two superconductors. Such an insulating layer forms a weak link between the superconductors which is referred to as the Josephson junctions. The effects observed by Josephson are given as follows:
**DC**

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