The radius of a nucleus of mass number 27 is $R$. Which of the following is true about a nucleus whose radius is $2 R$ ?

The nucleus ${ }_{50}^{120} X$ undergoes the series of reactions given below:

$$ { }_Z^A X \xrightarrow{\alpha \text {-decay }} P \xrightarrow{\beta^{-} \text {-decay }} Q \xrightarrow{\alpha \text {-decay }} R $$

The number of neutrons in the nucleus $R$ is

In hydrogen spectrum, the shortest and longest wavelengths of Balmer series are $\lambda_1$ and $\lambda_2$ respectively. The Rydberg constant of hydrogen is

$\alpha$-decay of a parent nucleus $X$ results in a daughter nucleus $Y$. If $m_x, m_y$ and $m_\alpha$ are the masses of the parent nucleus, the daughter nucleus and the $\alpha$-particles respectively, then the net kinetic energy gained in the process is