Calculate Q-Value of the reaction:

Take 

u and 

A piece of wood from the ruins of an ancient dwelling was found to have a ¹⁴C activity of 14 disintegrations per minute per gram of its carbon content. The ¹⁴C activity of living wood is 16 disintegrations per minute per gram. How long ago did the tree die from which the wood sample came? Take half-life of radiocarbon as 5760 years.

Establish the relation for binding energy per nucleon for nuclei. Calculate the value of binding energy per nucleon for Given:

Mass of Ni : 63.9280 u

Mass of proton : 1.007825 u

Mass of neutron : 1.008665 u

Is this nucleus stable?

The half life of ⁵¹Cr is 27.70 days. After how many days will only 10% of the element be left over?

Show that, for a symmetric potential function (V(x) = V(-x)), the parity operator commutes with the Hamiltonian. What is the parity of the of the following eigenfunctions of a symmetric potential well of width 2a: (i)  and (ii)

The refractive index of the core and cladding materials of an optical fibre is 1.52 and 1.46, respectively. Calculate the critical angle, numerical aperture and acceptance angle at the air-fibre interface.

With the help of a labeled diagram, discuss lasing action of a He-Ne laser.

A particle encounters a step potential of height . V₀ What is the reflection and transmission coefficient if E = 1.5V₀ ? Show that R + T = 1.

Define numerical aperture and angle of acceptance. An optical fiber has a numerical aperture of 0.20 and cladding refractive index of 1.59. Calculate the refractive index of the core material and the acceptance angle of the fibre in water whose refractive index is 1.33.

The eigenfunction of a particle confined in a box of length L ( 0  x  L ) is

Calculate and the probability of finding the particle between x = 0 and x = L / 4 .

Discuss applications of lasers in medicine and communication.

Diffraction limits the image forming capability of optical devices'. Discuss the authenticity of this statement for the particular case of a microscope.

The quantum mechanical wave function for a particle isv given by

Determine (i) the normalization constant N and(ii) the most probable position of the particle.

A vertical single and double slits and illuminated by a point source. Discuss the salient features of their Fraunhofer diffraction patterns. Also, obtain an expression for intensity distribution in case of double slit.

Explain how Michelson interferometer is used to determine the wavelength of light.

i) Show that the radius of a dark Newton's ring is directly proportional to the square root of the radius of curvature of the lens used.

ii) Newton's rings are formed in reflected light of wavelength 5890×10-8 cm with a liquid between the plane and curved surfaces. The diameter of the fifth ring is 0.3 cm and the radius of curvature of the curved surface is 100 cm. Calculate the refractive index of the liquid, when the ring is bright.

Using Heisenberg's Uncertainty Principle explain whether a particle trapped inside a one dimensional box of finite length can be at rest.

Calculate the de Broglie wavelength of a ⁸⁷Rb atom that has been laser cooled to 200 µK. (Assume that the kinetic energy is 3/2k_BT).

Determine the wavelengths of the photons scattered at (i) 60° and (ii) 90° when X- rays of wavelength 4.5 pm are scattered from a target.

A star emits light with wavelength 420 nm. An observer on earth measures the wavelength of the light received from the star to be 600 nm. Calculate the speed with which the star is moving.