Electrons in hydrogen atom first jump from third excited state to second excited state and then from second excited state to the first excited state. The ratio of ${\lambda }_1\backslash lambda\_1$ and ${\lambda }_2\backslash lambda\_2$ emitted in the two cases is

The binding energy of a hydrogen-like atom in ground state is 217.6 eV. An electron having energy of 130 eV is incident on the atom. Then the energy of the electron emerging after interacting with this atom is

The ratio of wavelength $H_{\alpha }H\_\backslash alpha$ and $H_{\beta }H\_\backslash beta$ lines of Paschen’s series is of the order of

The ratio of minimum to maximum wavelength in Balmer series is

The ratio of the longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

A critical potential for hydrogen is 13.05 V. A hydrogen atom is bombarded by an electron of corresponding energy. Then the wavelength of radiation emitted by the hydrogen atom is

Beta rays emitted by a radioactive material are

Half-life of a radioactive substance A is 4 day.s The probability that a nucleus will decay in two half-lives is

10 milligrams of a radioactive material of half-life two years are kept in a store for four years. Then the amount of the material remaining unchanged is

One milligram of thorium emits $22\alpha 22\backslash ,\backslash alpha$ particle per unit solid angle per minute. The half-life of thorium is of the order of