A radioactive nucleus $\mathrm{n}_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$, after one half-life of $n_1$ ?

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $$2: 1$$. After disintegration they will move :

The energy released in the fusion of $$2 \mathrm{~kg}$$ of hydrogen deep in the sun is $$E_H$$ and the energy released in the fission of $$2 \mathrm{~kg}$$ of $${ }^{235} \mathrm{U}$$ is $$E_U$$. The ratio $$\frac{E_H}{E_U}$$ is approximately: (Consider the fusion reaction as $$4_1^1H+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{~MeV}$$, energy released in the fission reaction of $${ }^{235} \mathrm{U}$$ is $$200 \mathrm{~MeV}$$ per fission nucleus and $$\mathrm{N}_{\mathrm{A}}= 6.023 \times 10^{23})$$

A hydrogen atom in ground state is given an energy of $$10.2 \mathrm{~eV}$$. How many spectral lines will be emitted due to transition of electrons?