assume that there is no repulsive force between the electrons in an atom but the force between positive and negative charges is given by Coulomb's law as usual.Under such circumstances, calculate the ground state energy of a He-atom.

(i) The radius of the innermost electron orbit of a hydrogen atom is \({ r }_{ 1 }=5.3\times 10^{ -11 }\) Calculate its radius in n=2 orbit.
(ii) The total energy of an electron in the second excited state of the hydrogen atom is -1.51eV. Find out its 
(a) kinetic energy and 
(b) potential energy in this state

Consider a radioactive nucleus A which decays to a stable nucleus C through the following sequence:
  A \(\longrightarrow \) B \(\longrightarrow \) C
where, B is an intermediate nuclei, which is also radioactive. Considering that there are N₀ atoms of A initially, plot the graph showing the variation of number of atoms of A and B versus time.

A 12.5eV electron beam is used to bombard f = gaseous hydrogen at room temperature. Upto which energy level the H-atoms would be excited? Calculate the wavelengths of the first member of Lyman and first member of Balmer series.

The deuteron id bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the force between neutron and proton in deuteron as given in the form a coulomb potential but with an effective charge' F=\(\frac { 1 }{ { 4\pi \varepsilon }_{ 0 } } .\frac { { e }^{ '2 } }{ r } .\) Estimate the value of (e^' /e) given that the binding energy of a deuteron is 2.2MeV.