A nucleus breaks into two nuclear parts, which have their velocity ratio $$2: 1$$. The ratio of their nuclear radii will be

Ratio centripetal acceleration for an electron revolving in 3^rd and 5^th Bohr orbit of hydrogen atom is

When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes

'$$\lambda_1$$' is the wavelength of series limit of Lyman series, '$$\lambda_2$$' is the wavelength of the first line line of Lyman series and '$$\lambda_3$$' is the series limit of the Balmer series. Then the relation between $$\lambda_1, \lambda_2$$ and $$\lambda_3$$ is