The following diagram indicates the energy levels of a certain atom when the system moves from $2E$ level to $E$, emitting a photon of wavelength $\lambda $. The wavelength of photon produced during its transition from $\frac{4E}{3}$ level to $E$ is

The wavelength of the first line of Balmer series of hydrogen atom is $\lambda \,\mathop A\limits^o $. The wavelength of this line of a double ionised lithium atom $(Z = 3)$is

If radiation of allow wavelengths from ultraviolet to infrared is passed through hydrogen agas at room temperature, absorption lines will be observed in the :

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number $Z$ of hydrogen like ion is

The wavelength of ${K_\alpha }$ line for an element of atomic number $29$ is $\lambda $ . Then the wavelength of ${K_\alpha }$ line for an element of atomic no $15$ is (Take mosley‘s constant $b = 1$ for both elements)

An alpha nucleus of energy $\frac{1}{2}mv^2$ bombards a heavy nuclear target of charge $Ze.$ Then the distance of closest approach for the alpha nucleus will be proportional to