The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first energy level and (b) highest energy level to second level is

If 'T' is the half life of a radioactive substance then its instantaneous rate of change of activity is proportional to

Radius of first orbit in H -atom is ' $a_0$ ' Then, de-Broglie wavelength of electron in the third orbit is

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' $r_0$ ' is the radius of the ground state orbit, ' $m$ ' is the mass, ' e ' is the charge on the electron and ' $\varepsilon_0$ ' is the permittivity of vacuum, the speed of the electron is