In the given reaction

$${ }_z \mathrm{X}^A \rightarrow{ }_{z+1} \mathrm{Y}^A \rightarrow{ }_{z-1} \mathrm{~K}^{A-4} \rightarrow{ }_{z-1} \mathrm{~K}^{\mathrm{A}-4}$$

radioactive radiations are emitted in the sequence

A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is