A radioisotope X with a half-life 1.4x109 yr decays into Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1:7. The age of the rock is
1. 1.96x109 yr
2. 3.92x109 yr
3. 4.20x109 yr
4. 8.40x109 yr
A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per nucleon is: (given 1 u = 931 MeV)
1. 2.67 MeV
2. 26.7 MeV
3. 6.675 MeV
4. 13.35 MeV
If the nuclear radius of A27l is 3.6 Fermi, the approximate nuclear radius of C64u in Fermi is
1. 2.4
2. 1.2
3. 4.8
4. 3.6
A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40g of A1 and 160g of A2. The amount of the two in the mixture will become equal after
1. 60 s
2. 80 s
3. 20 s
4. 40 s
The half-life of a radioactive nucleus is 50 days. The time interval (t2-t1) between the time t2 when 23 of it has decayed and the time t1 when 13 of it had decayed is:
1. 30 days
2. 50 days
3. 60 days
4. 15 days
Fusion reaction takes place at high temperature because
1. atoms get ionised at high temperature
2. kinetic energy is high enough to overcome the Coulomb repulsion between nuclei
3. molecules break up at high temperature
4. nuclei break up at high temperature
Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t=0, the number of P species are 4N0 and that of Q is N0. Half-life of P(for conversion to R) is 1 min whereas that of Q is 2 min. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be:
1. 3N0
2. 9N02
3. 5N02
4. 2N0
The mass of a L73i nucleus is 0.042u less than the sum of the masses of its nucleons.The binding energy per nucleon of L73i nucleus is nearly
(a) 46 MeV (b) 5.6 MeV
(c) 3.9 MeV (d) 23 MeV
The activity of a radioactive sample is measured as N0 counts per minute at t=0 and N0/e counts per minute at t=5 min.The time (in minute) at which the activity reduces to half its value is
(1) loge2/5
(2) 5loge 2
(3) 5 log10 2
(4) 5 loge 2
The decay constant of a radio isotope is λ. If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1-t2) is:
1. A1t1-A2t2
2. A1-A2
3. (A1-A2)λ
4. λ(A1-A2)