If 917 $$\mathop A\limits^o $$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ___________ $$\mathop A\limits^o $$.

The decay constant for a radioactive nuclide is 1.5 $$\times$$ 10$$^{-5}$$ s$$^{-1}$$. Atomic weight of the substance is 60 g mole$$^{-1}$$, ($$N_A=6\times10^{23}$$). The activity of 1.0 $$\mu$$g of the substance is ___________ $$\times$$ 10$$^{10}$$ Bq.

The ratio of wavelength of spectral lines $$\mathrm{H}_{\alpha}$$ and $$\mathrm{H}_{\beta}$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$x$$ is _________.

A nucleus with mass number 242 and binding energy per nucleon as $$7.6~ \mathrm{MeV}$$ breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as $$8.1 ~\mathrm{MeV}$$, the total gain in binding energy is _________ $$\mathrm{MeV}$$.