A $$12.5 \mathrm{~eV}$$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

The energy of $$\mathrm{He}^{+}$$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $$-13.6 ~\mathrm{eV})$$ :

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $$\lambda_{A}$$ and $$\lambda_{B}$$ are decay constants of A and B respectively, then choose the correct relation from the given options.

The half life of a radioactive substance is T. The time taken, for disintegrating $$\frac{7}{8}$$th part of its original mass will be: