Estimate the radius of the gold nucleus,when alpha particle of eneryg 6 Me V is incident at its centre and gets deflected through `180^@`.Given that atmic number of gold=79.

Calculate the impact parameter of 5 MeV alpha particle scattered by 10^@ ,when it approaches a gold nucleus.

An alpha particle (_2He^4) is moving directly towards a stationary gold nucleus (_(79)Au^(197)) .The alpha -particle and the gold nucleus may be considered to be solid spheres with the charge and mass concentrated at the centre of each sphere.When the two spheres are just toching,the sepaation of their centres is 9.6 xx 10^(-15) m . the alpha particle and the gold nucleus may be assumed to be an isolatedd system.Calculate for the alpha particle just in contact with the gold nucleus, its electric potential energy.

In Geiger-Marsden experiment,a 5 MeV alpha -particle is scattered through 180^@ from the gold foil.If the atomic number of gold is 79 ,find the distance of closet appraoch to the gold nucleus.

In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structureslike trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by (Ypir^4)/(4R) . Y is the Young's modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neuttral surface). EStimate the critical height of a tree for a given radius of the trunk.

Calculate the electric potential at the surface of a gold nucleus. Given radius of nucleus = 6.6 xx 10^-15 m and atomic wight of gold is 79.