When a hydrogen atom transitions from $n=2$ to $n=1$, it emits a photon. The recoil speed of the atom is $\frac{x}{5} \,m/s$. Find the value of $x$. (Use: mass of hydrogen atom $= 1.6 \times 10^{-27} \,kg$)

The ground state energy of a hydrogen atom is $-13.6 \text{ eV}$. When its electron is in the first excited state,its excitation energy is:

$\frac{x}{x+4}$ is the ratio of energies of photons produced due to the transition of an electron of a hydrogen atom from its $(i)$ third permitted energy level to the second level and $(ii)$ the highest permitted energy level to the second permitted level. The value of $x$ will be.

Explain the formulas for the energy of an electron in an atom revolving around the nucleus in different orbits.

In the $n^{th}$ orbit,the energy of an electron is given by $E_n = -\frac{13.6}{n^2} \text{ eV}$ for a hydrogen atom. The energy required to excite the electron from the first orbit $(n=1)$ to the second orbit $(n=2)$ will be..... eV.

The figure shows the energy levels $P, Q, R, S$ and $G$ of an atom,where $G$ is the ground state. $A$ red line in the emission spectrum of the atom is obtained by an energy level transition from $Q$ to $S$. $A$ blue line can be obtained by which of the following energy level transitions?