A ancient discovery found a sample, where $$75 \%$$ of the original carbon ($$\mathrm{C}^{14}$$) remains. Then the age of the sample is $$\binom{T_{\frac{1}{2}}\left(C^{14}\right)=5730 \text { years, } \ln 0.5=-0.7}{\ln (0.75)=-0.3} $$

A hydrogen atom at the ground level absorbs a photon and is excited n = 4 level. The potential energy of the electron in the excited state is

The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius 6 fermi is

Energy of a stationary electron in the hydrogen atom is $$E=\frac{13.6}{n^2} \mathrm{~eV}$$, then the energies required to excite the electron in hydrogen atom to (a) its second excited state and (b) ionised state, respectively.