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. \(-6.8~\text{eV}\)

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

(a) $\frac{1}{Ze}$                              (b) $v^2$

(c) $\frac{1}{m}$                               (d) $\frac{1}{v^4}$

The electron in the hydrogen atom jumps from excited state $\left(n=3\right)$ to its ground state $\left(n=1\right)$ and the photons thus emitted irradiate a photosensitive material. If the work function of the material is $5.1 \mathrm{eV},$ the stopping potential is estimated to be (the energy of the electron in the nth state ${\mathrm{E}}_{\mathrm{n}}=-\frac{13.6}{{\mathrm{n}}^2}\mathrm{eV}$)

1. $5.1 \mathrm{V}$                                               

2. $12.1 \mathrm{V}$

3. $17.2 \mathrm{V}$                                             

4. $7 \mathrm{V}$

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 the closest approach is \(r_0.\) What is the energy of the projectile?

The ionization energy of the electron in the hydrogen atom in its ground state is 13.6 eV. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths. Maximum wavelength of emitted radiation corresponds to the transition between

(a) n=3 to n=2 states

(b) n=3 to n=1 states

(c) n=2 to n=1 states

(d) n=4 to n=3 states

The ground state energy of hydrogen atom is -13.6 eV. When its electron is in the first excited state, its excitation energy is:

(1) 3.4 eV                               

(2) 6.8 eV

(3) 10.2 eV                             

(4) zero 

In the phenomenon of electric discharge through gases at low pressure, the coloured glow in the tube appears as a result of:

(1) excitation of electrons in the atoms 

(2) the collision between the atoms of the gas 

(3) the collisions between the charged particles emitted from the cathode and the atoms of the gas 

(4) the collision between different electrons of the atoms of the gas 

The ratio of momenta of an electron and an $\mathrm{}$\(\alpha \text-\)particle which are accelerated from rest by a potential difference of \(100~\text{V}\) is:
1. \(1\)
2. \(\sqrt{\frac{2m_e}{m_{\alpha}}}\)
3. \(\sqrt{\frac{m_e}{m_{\alpha}}}\)
4. \(\sqrt{\frac{m_e}{2m_{\alpha}}}\)

The fact that electric charges are integral multiples of the fundamental electronic charge was proved experimentally by 
(1) Planck                   

(2) J.J. Thomson

(3) Einstein                 

(4) Millikan

The specific charge of an electron is 

(a) $1.6\times {10}^{-19}$ coulomb

(b) $4.8\times {10}^{-10}$ stat coulomb

(c) $1.76\times {10}^{11}$ coulomb/kg

(d) $1.76\times {10}^{-11}$  coulomb/kg