Atoms

Consider an electron in the n=3 orbit of a hydrogen-like atom with atomic number Z. At absolute temperature T, a neutron having thermal energy kBT has the same de Broglie wavelength as that of this electron. If this temperature is given by T= Z2h2 2a02mNkB, (where h is the Planck's constant, kB is the Boltzmann constant, mN is the mass of the neutron and a0 is the first Bohr radius of hydrogen atom) then the value of is

A particle of mass m is moving in a circular orbit under the influence of the central force F(r)=-kr, corresponding to the potential energy V(r)=kr2/2, where k is a positive force constant and r is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by L=n , where =h/(2 ), h is the Planck's constant, and n a positive integer. If v and E are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

1. r2=n 1mk
2. v2=n km3
3. Lmr2= km
4. E= n 2 km