Activity of a radioactive sample decreases to $\left(\dfrac{1}{4}\right)^{th}$ of its original value in 4 days. Then in 16 days its activity will become $x$ times the original value. The value of $x$ is

An electron in the hydrogen atom jumps from $n^{th}$ energy state to the ground state. The wavelength so emitted illuminates a photosensitive material having work function $2.65$ eV. If the maximum kinetic energy of the emitted photoelectrons is $10.1$ eV, then the value of '$n$' is

The angular momentum of an electron in Bohr's hydrogen atom having energy $(-0.544)$ eV is
($h$ = Planck's constant)

If the ionisation energy for the hydrogen atom is $13.6$ eV, then the energy required to excite it from the ground state to the next higher state is nearly