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

A sample of radioactive element contains $$8 \times 10^{16}$$ active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is