from the relation `R=R_0A^(1//3)`, where `R_0` is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e., independent of A ).

Show that the density of nuclear mass is constant for all isotopes.

The graph of 1n (R/R_0) versus 1n A (R = radius of a nucleus and A = its mass number) is

consider the relation R ={ (x,2x -1 ) |x in A }, where A = { 1,-1,3 } write the range of R .

Differentiate a^(x) w.r.t. x, where a is a positive constant.

In terms of Rydberg constant R, the wave number of the first Balmer line is

Determine the domain and range of the relation R where R = { (x,x ^3) : x is a prime number less than 15 }.

If z=z_0+A( bar z -( bar z _0)), w h e r eA is a constant, then prove that locus of z is a straight line.

A small particle of mass m move in such a way the potential energy U = (1)/(2) m^(2) omega^(2) r^(2) where omega is a constant and r is the distance of the particle from the origin. Assuming Bohr's model of quantization of angular momentum and circular orbits , show that radius of the nth allowed orbit is proportional to √n

What is the ratio of nuclear densities of two nucleus having mass numbers in the ratio 1 : 2 ?

The potential energy of a particle in a force field is : U= A/r^2-B/r^1 , where A and B are positive constant and r is the centre of the field. For stable equilibrium, the distance of the particle is :