A hydrogen atom in its ground state is irradiated by light of wavelength 970$$\mathop A\limits^o $$.

Taking hc = 1.237 $$\times$$ 10^$$-$$6 eVm and the ground state energy of hydrogen atom as $$-$$ 13.6 eV, the number of lines present in the emission spectrum is

The isotope $$_5^{12}B$$ having a mass 12.014 u undergoes $$\beta $$-decay to $$_6^{12}C$$. $$_6^{12}C$$ has an excited state of the nucleus ($$_6^{12}C$$*) at 4.041 MeV above its ground state. If $$_5^{12}B$$ decays to $$_6^{12}C$$*, the maximum kinetic energy of the $$\beta$$-particle in units of MeV is (1u = 931.5 MeV/c², where c is the speed of light in vacuum).

For a radioactive material, its activity A and rate of change of its activity R are defined as $$A = - {{dN} \over {dt}}$$ and $$R = - {{dA} \over {dt}}$$, where N(t) is the number of nuclei at time t. Two radioactive source P(mean life $$\tau $$) and Q (mean life 2$$\tau $$) have the same activity at t = 0. Their rate of change of activities at t = 2$$\tau $$ are R_P and R_Q, respectively. If $${{{R_P}} \over {{R_Q}}} = {n \over e}$$, then the value of n is

An electron in an excited state of Li²⁺ ion has angular momentum $${{3h} \over {2\pi }}$$. The de Broglie wavelength of the electron in this state is p$$\pi$$a₀ (where a₀ is the Bohr radius). The value of p is