An $\mathrm{}$\(\alpha\text -\)particle of \(5 ~\text{MeV}\) energy strikes with a nucleus of uranium at stationary at a scattering angle of \(180^\circ.\) The nearest distance up to which the \(\alpha\text -\)particle reaches the nucleus will be of the order of:
1. \(1~\mathring A     \)         
2. \(10^{- 10} ~\text{cm}\)
3. \(10^{- 12} ~\text{cm}\)
4. \(10^{- 15} ~\text{cm}\)$$

The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is

1. 1/2                2. 2/137
3. 1/137            4. 1/237

An energy of 24.6 eV is required to remove one of the electrons from a neutral helium atom. The energy (in eV) required to remove both the electrons from a neutral helium atom is 
(a) 79.0              (b) 51.8
(c) 49.2              (d) 38.2

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The orbital angular momentum is increased by-  (Given Planck constant h = $6.6\times {10}^{-34}$ J-sec)

1. $1.05\times {10}^{-34}$ J-sec                 2. $3.16\times {10}^{-34}$ J-sec
3. $2.11\times {10}^{-34}$ J-sec                 4. $4.22\times {10}^{-34}$J-sec

Hydrogen (H), deuterium (D), singly ionized helium and doubly ionized lithium all have one electron around the nucleus. Consider n =2 to n = 1 transition. The wavelengths of emitted radiations are ${\mathrm{\lambda }}_1,{\mathrm{\lambda }}_2,{\mathrm{\lambda }}_3$ and ${\mathrm{\lambda }}_4$ respectively. Then approximately 
(a) ${\mathrm{\lambda }}_1={\mathrm{\lambda }}_2=4{\mathrm{\lambda }}_3=9{\mathrm{\lambda }}_4$                             (b) $4{\mathrm{\lambda }}_1=2{\mathrm{\lambda }}_2=2{\mathrm{\lambda }}_3={\mathrm{\lambda }}_4$
(c) ${\mathrm{\lambda }}_1=2{\mathrm{\lambda }}_2=2\sqrt{2}{\mathrm{\lambda }}_3=3\sqrt{2}{\mathrm{\lambda }}_4$                 (d) ${\mathrm{\lambda }}_1={\mathrm{\lambda }}_2=2{\mathrm{\lambda }}_3=3\sqrt{2}{\mathrm{\lambda }}_4$

A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The wavelength of required radiation for exciting electron from first to third Bohr orbit in ${\mathrm{Li}}^{++}$ will be (Ionisation energy of hydrogen atom is 13.6eV) 
(a) 182.51 Å                 (b) 177.17 Å
(c) 142.25 Å                 (d) 113.74 Å

The ionisation potential of H-atom is  13.6 V. When it is excited from ground state by monochromatic radiations of $970.6 \stackrel{0}{\mathrm{A}}$, the number of emission lines will be (according to Bohr’s theory) 
(1) 10           

(2) 8

(3) 6             

(4) 4

A neutron with velocity V strikes a stationary deuterium atom. Its kinetic energy changes by a factor of 
(1) $\frac{15}{16}$             

(2) $\frac{1}{2}$

(3) $\frac{2}{1}$               

(4) None of these

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength $\mathrm{\lambda }$ (given in terms of the Rydberg constant R for the hydrogen atom) equal to

(1) 9/(5R)                 
(2) 36/(5R)
(3) 18/(5R)               
(4) 4/R