In Balmer series, wavelength of the $$2^{\text {nd }}$$ line is '$$\lambda_1$$' and for Paschen series, wavelength of the $$1^{\text {st }}$$ line is '$$\lambda_2$$', then the ratio '$$\lambda_1$$' to '$$\lambda_2$$' is

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

The wavelength of radiation emitted is '$$\lambda_0$$' when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $$\frac{20}{x} \lambda_0$$. The value of $$x$$ is

According to Bohr's theory of hydrogen atom, the total energy of the electron in the $$\mathrm{n}^{\text {th }}$$ stationary orbit is