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

what is the respective number of $\alpha$ and $\beta$-particles emitted in the following radioactive decay

${}^{200}X_{90}\to {}^{168}Y_{80} ?$ [1995]

(1) 6 and 8               (2) 6 and 6           (3) 8 and 8          (4) 8 and 6   

The half-life of radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay [Raj - PMT 1999; AIEEEE 2004]

(1) 3244 years             (2) 6488 years           (3) 4866 years        (4) 811 years

The mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit) The binding energy of ${}_{2}H{e}^4$ is (mass of helium nucleus = 4.0015 u) [2003]

(1) 28.4 MeV          (2) 0.061 u             (3) 0.0305 J          (4) 0.0305 erg

The binding energies of the nuclei A and B are $E_a and E_b$ respectively. Three atoms of the element B fuse to give one atom of element A and an energy Q is released.Then $E_a, E_b$ and Q are related as

(1) $E_a-3E_b=Q$                    (2) $3E_b-E_a=Q$

(3) $E_a+3E_b=Q$                    (4) $E_b+3E_a=Q$

A free neutron decays into a proton, an electron and [1997]

(1) a beta particle                 (2) an alpha particle

(3) an antineutrino                (4) a neutrino

In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is 

(1) $\frac{1}{e^n}$            (2) $e^n$            (3) $1-\frac{1}{e^n}$            (4) ${\left(\frac{1}{e-1}\right)}^n$

The activity of a radioactive sample is measured as 9750 counts/min at t = 0 and as 975 counts/min at t = 5 min. The decay constant is approximately [1997]

(1) 0.922 / min            (2) 0.691 / min           (3) 0.461 / min            (4) 0.230 / min

The energy equivalent of one atomic mass unit is [1992]

(1) $1.6\times {10}^{-19} J$                   (2) $6.02\times {10}^{23} J$

(3) 931 MeV                             (4) 9.31 MeV

Solar energy is due to

1. fusion reaction

2. fission reaction

3. combustion reaction

4. chemical reaction