In a radioactive decay chain, the initial nucleus is $${}_{90}^{232}$$Th. At the end there are 6 $$\alpha $$-particles and 4 $$\beta $$-particles which are emitted. If the end nucleus is $${}_Z^A$$X, A and Z are given by :

A particle of mass m moves in a circular orbit in a central potential field U(r) = $${1 \over 2}$$ kr². If Bohr 's quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $$\lambda $$. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$$\mathop A\limits^ \circ $$. The radius of the atom in the excited state, in terms of Bohr radius a₀ will be : (hc = 12500 eV$$\mathop A\limits^ \circ $$)