1. A radioactive nucleus \({}^{A}_{z}X\) undergoes spontaneous decay inthe sequence
\({}^{A}_{z}X \, \rightarrow \, {}_{z-1}B \, \rightarrow \, {}_{z-3}C \, \rightarrow \, {}_{z-2}D\) where Z is the atomic number of element X. The possible decay particles in the sequence are

(1).\(\alpha,\, \beta^-,\, \beta^+\)

(2). \(\alpha,\, \beta^+,\, \beta^-\)

(3). \(\beta^+,\, \alpha,\, \beta^-\)

(4). \(\beta^-,\, \alpha,\, \beta^+\)

2. The half-life of a radioactive nuclide is 100 h. The fraction of original activity that will remainafter 150 h would be

(1).\(\displaystyle \frac{1}{2}\)

(2). \(\displaystyle \frac{1}{2 \sqrt{2}}\)

(3). \(\displaystyle \frac{2}{3}\)

(4). \(\displaystyle \frac{2}{3 \sqrt{2}}\)

3. What happens to themass number and atomic number of an element when it emits \(\gamma\) -radiation?

(1).Mass number decreases by four andatomic number decreases by two.

(2). Mass number and atomic numberremain unchanged.

(3). Mass number remains unchanged,while atomic number decreases byone.

(4). Mass number increases by four andatomic number increases by two.

4. The half-life of a radioactive sample under going \(\alpha\) -decay is 1.4 x 10¹⁷ s. If the number of nuclei in the sample is 2.0 x 10²¹. The activity of the sample is nearly

(1).10⁴ Bq

(2). 10⁵ Bq

(3). 10⁶ Bq

(4). 10³ Bq

5. The rate of radioactive disintegration at an instant for a radioactive sample of half life2 . 2 × 10⁹ s is 10¹⁰ s⁻¹ . The number of radioactive atoms in that sample at that instant is

(1).3.17×10²⁰

(2). 3.17×10¹⁷

(3). 3.17×10¹⁸

(4). 3.17×10¹⁹

6. a-particle consists of

(1).2 electrons, 2 protons and 2 neutrons

(2). 2 electrons and 4 protons only

(3). 2 protons only

(4). 2 protons and 2 neutrons only

7. For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

(1).30

(2). 10

(3). 20

(4). 15

8. Radioactive material A has decay constant \(8 \lambda\) and material B has decay constant \(\lambda\). Initially, they have same number of nuclei. After what time, the ratio of number ofnuclei of material B to that A will be 1\e ?

(1).\(\displaystyle \frac{1}{\lambda}\)

(2). \(\displaystyle \frac{1}{7 \lambda}\)

(3). \(\displaystyle \frac{1}{8\lambda}\)

(4). \(\displaystyle \frac{1}{9\lambda}\)

9. The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is

(1).15

(2). 30

(3). 45

(4). 60

10. A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the binding energyin the process is

(1).0.9 MeV

(2). 9.4 MeV

(3). 804 MeV

(4). 216 MeV

11. The energy equivalent of 0.5 g of a substance is

(1).4.5 × 10¹³ J

(2). 1.5 × 10¹³ J

(3). 0.5 × 10¹³ J

(4). 4.5 × 10¹⁶ J

12. When a uraniumisotope \(\displaystyle {}^{235}_92U\) is bombarded with a neutron, itgenerates \(\displaystyle {}^{89}_{36}Kr\), three neutrons and

(1).\(\displaystyle {}^{91}_{40}Zr\)

(2). \(\displaystyle {}^{101}_{36}Kr\)

(3). \(\displaystyle {}^{103}_{36}Kr\)

(4). \(\displaystyle {}^{144}_{56}Ba\)

13. The binding energy per nucleon of \(_3Li^7\) and \(_2He^4\) nuclei are 5.60 MeV and 7.06 MeV, respectively. In the nuclear reaction \(_3Li^7 + _1H^1 \rightarrow _2He^2 + _2He^4 + Q\), the value of energy Q released is

(1).19.6MeV

(2). -2.4 MeV

(3). 8.4 MeV

(4). 17.3 MeV

14. A radio isotope X with a half life 1.4 x 10sup9 yr decays of Y which is stable. A sample of the rock from a cave was found to contain X and Y in teh ratio 1:7. The age of the rock is

(1).1.96 x 10^{9 yr}

(2). 3.92 x 10^{9 yr}

(3). 4.20 x 10^{9 yr}

(4). 8.40 x 10^{9 yr}

15.
In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are:

(1).288, 82

(2). 286,81

(3). 280, 81

(4). 286, 80

16. The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to \(\displaystyle \left(\frac{1}{16}\right)^{th}\) of its initial value?

(1).40 minutes

(2). 60 minutes

(3). 80 minutes

(4). 20 minutes

17. In the given nuclear reaction, the element X is :
\(\displaystyle ^{23} _{11} \,Na \rightarrow\,X+e^+ + v\)

(1).\(\displaystyle ^{23} _{11} \,Na \)

(2). \(\displaystyle ^{23} _{10} \,Ne \)

(3). \(\displaystyle ^{22} _{10} \,Ne \)

(4). \(\displaystyle ^{22} _{12} \,Mg \)

18. A nucleus of mass number of 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is :

(1).1:01

(2). 4:05

(3). 5:04

(4). 25:16:00

19. If radius of the \(_{13}\text{Al}^{27}\) nucleus is taken to be \(R_{\text{Al}}\), then the radius of \(_{53}\text{Te}^{125}\) nucleus is nearly

(1).\(\displaystyle \left(\frac{53}{13} \right)^{\frac{1}{3}} R_{Al}\)

(2). \(\displaystyle \frac{5}{3}R_{\text{Al}}\)

(3). \(\displaystyle \frac{3}{5}R_{\text{Al}}\)

(4). \(\displaystyle \frac{13}{53}R_{\text{Al}}\)