In a radioactive substance at t = 0, the number of atoms is 8$\times {10}^4$, its half-life period is 3 yr. the number of atoms $1\times {10}^4$ will remain after interval [UP CPMT 2010]

(1) 9 yr              (2) 8 yr              (3) 6 yr             (4) 24 yr

A nucleus ${}_{n}X_{{}_m}$ emits one $\alpha$ and two $\beta -$particles. The resulting nucleus is

(1) ${}_{n}X_{m-4}$         (2) ${}_{n-2}Y_{m-4}$           (3) ${}_{n-4}Z_{m-4}$            (4) None of these

The half-life period of a radioactive substance is 6 h.  After 24 h activity is 0.01 $\mu$Ci, what was the initial activity? 

(1) 0.04 $\mu$Ci         (2) 0.08 $\mu$Ci           (3) 0.24 $\mu$Ci              (4) 0.16 $\mu$Ci

The relationship between disintegration constant $\left[\lambda \right]$ and half-life [T] will be:

(1) $\lambda =\frac{{\log }_{10} 2}{T}$                    (2) $\lambda =\frac{{\log }_e 2}{T}$

(3) $\lambda =\frac{T}{{\log }_e 2}$                      (4) $\lambda =\frac{{\log }_2 e}{T}$

If the nuclear force between two protons, two neutrons and between proton and neutron is denoted by $F_{pp}, F_{nn} and F_{pn}$ respectively, then [1991]

(1) $F_{pp}\approx F_{nn}\approx F_{pn}$

(2) $F_{pp}\ne F_{nn} and F_{pp}=F_{nn}$

(3) $F_{pp}=F_{nn}=F_{pn}$

(4) $F_{pp}\ne F_{nn}\ne F_{pn}$

In a given reaction,

${}_{Z}X_A\to {}_{Z+1}Y_A\to {}_{Z-1}K_{A-4}\to {}_{Z-1}K_{A-4}$

Radioactive radiations are emitted in the sequence of  

(1)  $\alpha , \beta , \gamma$       (2) $\gamma , \alpha , \beta$             (3) $\beta , \alpha , \gamma$            (4) $\gamma , \beta , \alpha$

If a proton and anti-proton come close to each other and annihilate, how much energy will be released?

Heavy water is used as a moderator in a nuclear reactor. The function of the moderator is 

(1) to control energy released in the reactor

(2) to absorb neutrons and stop the chain reaction

(3) to cool the reactor

(4) to slow down the neutrons to thermal energies

The binding energy per nucleon of deuterium and helium atom is 1.1 MeV and 7.0 MeV. If two deuterium nuclei fuse to form a helium atom, the energy released is 

(1) 19.2 MeV            (2) 23.6 MeV             (3) 26.9 MeV                (4) 13.9 MeV