The ratio of the kinetic energies of the electrons in the third and fourth excited states of hydrogen atom is

In $\beta^{-}$decay, a neutron transforms into a proton within the nucleus according to the equation :

neutron $\rightarrow$ proton $+\beta^{-}+x$

In this equation the particle represented by ' $x$ ' is

Two radioactive substances $A$ and $B$ have same number of initial nuclei. If the half lives of $A$ and $B$ are 1.5 days and 4.5 days respectively, then the ratio of the number of nuclei remaining in $A$ and $B$ after 9 days is

If the difference in the frequencies of the first and second lines of Lyman series of hydrogen atom is $f$, then the difference in frequencies of the first and second lines of Balmer series of hydrogen atom is