In the spectrum of hydrogen atom, the ratio of the longest wavelength in Lyman series to thelongest wavelength in the Balmer series is

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius $r$. The Coulomb force $\vec{F}$ between the two is

An electron having de-Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted $X$-ray is :

According to the classical electromagnetic theory, calculate the initial frequency of the light emitted by the electron revolving around a proton in hydrogen atom.

A proton is fired from very far away towards a nucleus with charge $Q=120 \ e$, where $e$ is the electronic charge. It makes a closest approach of $10 \ fm$ to the nucleus. The de Brogle wavelength (in units of $fm$ ) of the proton at its start is :

(take the proton mass, $m _0=(5 / 3) \times 10^{-27} kg , h / e =4.2 \times 10^{-15} J / s / C ; \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 m / F ; 1 fm =10^{-15} m$ ) 

The first line in the Lyman series has wavelength $\lambda $ . The wavlength of the first line in Balmer series is