The energy of a hydrogen atom in the ground state is \(-13.6~\text{eV}\). What is the energy of a \(\mathrm{He}^+\) ion in the first excited state?
1. \(-13.6~\text{eV}\)
2. \(-27.2~\text{eV}\)
3. \(-54.4~\text{eV}\)
4. \(-6.8~\text{eV}\)

In a Rutherford scattering experiment when a projectile of charge $Z_1$ and mass $M_1$ approaches a target nucleus of charge $Z_2$ and mass $M_2,$ the distance of closest approach is $r_0$. What is the energy of the projectile?

In the \(n^{th}\) orbit, the energy of an electron is \(E_{n}=-\frac{13.6}{n^2} ~\text{eV}\) for the hydrogen atom. What will be the energy required to take the electron from the first orbit to the second orbit?
1. \(10.2~\text{eV}\)
2. \(12.1~\text{eV}\)
3. \(13.6~\text{eV}\)
4. \(3.4~\text{eV}\)

A beam of fast-moving alpha particles were directed towards a thin film of gold. The parts \(A', B',\) and \(C'\) of the transmitted and reflected beams corresponding to the incident parts \(A,B\) and \(C\) of the beam, are shown in the adjoining diagram. The number of alpha particles in:

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquires as a result of photon emission will be:
(m is the mass of the hydrogen atom, \(R\) Rydberg constant and \(h\) Planck's constant)

Considering the \(3^{rd}\) orbit of \(\mathrm{He}^{+}\) (Helium ion), using the non-relativistic approach, the speed of the electron in this orbit will be: (Given: \(Z=2, K = 9\times 10^{9}\), and Planck's constant, \(h= 6.6\times10^{-34}\) J-s)
1. \(2.92\times 10^{8}\) m/s
2. \(1.46\times 10^{6}\) m/s
3. \(0.73\times 10^{8}\) m/s
4. \(3.0\times 10^{8}\) m/s

If an electron in a hydrogen atom jumps from the \(3\)rd orbit to the \(2\)nd orbit, it emits a photon of wavelength \(\lambda\). What will be the corresponding wavelength of the photon when it jumps from the \(4^{th}\) orbit to the \(3\)rd orbit?