${}_{86}{}^{222}\mathrm{A}\to {}_{84}{}^{210}\mathrm{B}$. In this reaction how many $\mathrm{\alpha }$ and $\mathrm{\beta }$ particles are emitted 
(a) 6$\mathrm{\alpha }$, 3$\mathrm{\beta }$          (b) 3$\mathrm{\alpha }$, 4$\mathrm{\beta }$ 
(c) 4$\mathrm{\alpha }$, 3$\mathrm{\beta }$          (d) 3$\mathrm{\alpha }$, 6$\mathrm{\beta }$  

The phenomenon of radioactivity is 
(1) Exothermic change which increases or decreases with temperature

(2) Increases on applied pressure

(3) Nuclear process does not depend on external factors

(4) None of the above

If half life of radium is 77 days. Its decay constant in day will be
(1) $3\times {10}^{-13}$/day           

(2) $9\times {10}^{-3}$/day

(3) $1\times {10}^{-3}$/day             

(4) $6\times {10}^{-3}$/day

Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion 5 billion years ago. The other was created in a nuclear reactor 5 minutes ago. The probability of decay during the next time is 
(1) Different for each nuclei

(2) Nuclei created in explosion decays first

(3) Nuclei created in the reactor decays first

(4) Independent of the time of creation

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) ${\mathrm{\lambda }}_1={\mathrm{\lambda }}_2=2{\mathrm{\lambda }}_3=3\sqrt{2}{\mathrm{\lambda }}_4$