Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2^nd and 4^th orbits of hydrogen atom ________.

The average energy released per fission for the nucleus of ${ }_{92}^{235} \mathrm{U}$ is 190 MeV . When all the atoms of 47 g pure ${ }_{92}^{235} \mathrm{U}$ undergo fission process, the energy released is $\alpha \times 10^{23} \mathrm{MeV}$. The value of $\alpha$ is $\_\_\_\_$ .

(Avogadro Number $=6 \times 10^{23}$ per mole)

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $\mathrm{n}^{\text {th }}$ energy state by emitting a photon of energy 2.86 eV . The integer value of n will be__________.

A star has $$100 \%$$ helium composition. It starts to convert three $${ }^4 \mathrm{He}$$ into one $${ }^{12} \mathrm{C}$$ via triple alpha process as $${ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}$$. The mass of the star is $$2.0 \times 10^{32} \mathrm{~kg}$$ and it generates energy at the rate of $$5.808 \times 10^{30} \mathrm{~W}$$. The rate of converting these $${ }^4 \mathrm{He}$$ to $${ }^{12} \mathrm{C}$$ is $$\mathrm{n} \times 10^{42} \mathrm{~s}^{-1}$$, where $$\mathrm{n}$$ is _________. [ Take, mass of $${ }^4 \mathrm{He}=4.0026 \mathrm{u}$$, mass of $${ }^{12} \mathrm{C}=12 \mathrm{u}$$]