1.(a) State experimental evidences for
i) strong repulsive force
ii) strong attractive force between atoms in a solid.
(b) A simple model for the oxygen molecule consists of two equal masses connected by a light spring . The atoms oscillate along their lines of centre while the midpoint of the spring remains fixed.
i) Write down an expression for the frequency of oscillation of one oxygen atom in terms of its mass m and the force constant K of one half of the spring.
How is K related to the force constant k of the whole spring?[the force constant is the force per unit extension.]
ii)From spectroscopic measurements of oxygen molecules ,it may be deduced that the frequency of oscillation of the molecule is about 4.7 x10^13 Hz. In what region of the electromagnetic spectrum does radiation of this frequency lie? What effective force constant k does this correspond to? [Relative atomic mass of oxygen =16 ]
2. (a)Draw, on the same horizontal axis, then sketch graphs to show hot the following quantities vary with separation r.
i) potential energy U
ii) Force F between atoms
Mark the positions corresponding to the equilibrium separation between atoms for both the graph.
iii) State the relationship between the potential energy and the force between two atoms.
iv)Use your graph of potential energy versus separation to explain the thermal expansion of a solid.
v) Explain why the atoms in a crystalline solid are arranged in regular and orderly manner .
b) The potential energy of a two –atom system is represented by
u= a/r^2 - b/r^6
where r is the separation between atoms a and b are constants.
Find r_0,the value of r at which U is a minimum in terms of a and b.
Find u_0, the potential energy of the system when r=r_0.
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