**NUCLEI QUIZ-22**

**NUCLEI QUIZ-22**

**Dear Readers,**

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts.

**Q1. Statement 1: To determine the age of certain very old organic samples, dating of the sample with radioactive isotopes having larger half-life is a better choice than with radioactive isotopes having smaller half-lives**

**Statement 2: The activity of a radioactive sample having smaller half-life is negligibly small after a very long time and hence makes it next to impossible to get detected**

Solution

(a)
If the half-life of a radioactive isotope is small as compared to the age of organic sample, then over the age of the sample the activity of radioactive isotope becomes very small and hence is impossible to detect. While this process will not arise if we use radioactive isotope having larger half-life for dating with organic samples

**Q2. Statement 1: _Z X^Aundergoes 2Î±-decays, 2Î²-decays and 2Î³-decays and the daughter product is _(Z-2) Y^(A-8)**

**Statement 2: In Î±-decay the mass number decreases by 4 and atomic number decrease by 2. In Î²-decay the mass number remains unchanged, but atomic number increases by 1 only**

Solution

(a)
In Î±=decay, the mass number decreases by 4 and atomic number decreases by 2. In Î²-decay, the mass number does not change but atomic number changes by 1.In Î±-decay the atomic and mass number remain unchanged.
The reaction can be summarised as
Thus, at a far extent reason explain assertion but not completely

**Q3.Statement 1: Energy is released in nuclear fission**

**Statement 2: Total binding energy of the fission fragments is larger than the total binding energy of the parent nucleus**

Solution
(b)
In a nuclear fission, when a bigger nucleus is fissioned into two light weight nuclei, then due to mass defect some energy is released. According to concept of binding energy, fission can occur because the total mass energy will decrease; that is ∆E_bn(binding energy) will increase. We see that for high mass nuclide (A=240), the binding energy per nucleon is about 7.6MeV/nucleon. For the middle weight nuclides (A=120), it is about 8.5 MeV/nucleon. Thus, binding energy of fission fragments is larger than the total binding energy of the parent nucleus

**Q6.Nuclei of a radioactive element X are being produced at a constant rate K and this element decays to a stable nucleus Y with a decay constant Î» and half-life T_(1/2). At time t=0, there are N_0 nuclei of the element X The number N_X of nuclei of X at time t=T_(1/2) is**

**Q7.A radionuclide with decay constant Î» is being produced in a nuclear reactor at a rate q_0 t per second, where q_0 is a positive constant and t is the time. During each decay, E_0 energy is released. The production of radionuclide starts at time t=0 259. Which differential equation correctly represents the above process?**

**Q8. Various rules of thumb have been proposed by the scientific community to explain the mode of radioactive decay by various radioisotopes. One of the major rules is called the n/p ratio. If all the known isotopes of the elements are plotted on a graph of number of neutrons (n) versus number of protons (p), it is observed that all isotopes lying outside of a ‘stable’ n/p ratio region are radioactive as shown in Various rules of thumb have been proposed by the scientific community to explain the mode of radioactive decay by various radioisotopes. One of the major rules is called the n/p ratio. If all the known isotopes of the elements are plotted on a graph of number of neutrons (n) versus number of protons (p), it is observed that all isotopes lying outside of a ‘stable’ n/p ratio region are radioactive as shown in The graph exhibits straight line behavior with unit slope up to p=25. Above p=25, those isotopes with an n/p ratio lying below the stable region usually undergo electron capture while those with n/p ratios lying above the stable region usually undergo beta decay. Very heavy isotopes (p>83) are unstable because of their relatively large nuclei and they undergo alpha decay. Gamma ray emission does not involve the release of a particle. It represents a change in an atom from a higher energy level to a lower energy level.**

**How would the radioisotope of magnesium with atomic mass 27 undergo radioactive decay?**

**Q9. The radionuclide ^56 Mn is being produced in a cyclotron at a constant rate P by bombarding a manganese target with deuterons. ^56 Mn has a half-life of 2.5 h and the target contains large number of only the stable manganese isotopes ^56 Mn. The reaction that produces ^56 Mn is ^56 Mn+d→ ^56 Mn+p After being bombarded for a long time, the activity of ^56 Mn becomes constant, equal to 13.86×10^10 s^(-1). (Use ln〖2=0.693;〗 Avagardo number =6×10^2; atomic weight of ^56 Mn=56 g mol^(-1).)**

**At what constant rate P,^56 Mn nuclei are being produced in the cyclotron during the bombardment?**

Solution

(b)
In equilibrium,
Rate of decay = rate of production

**Q10. Many unstable nuclei can decay spontaneously to a nucleus of lower mass but different combination of nucleons. The process of spontaneous emission of radiation is called radioactivity. Three types of radiations are emitted by radioactive substance Radioactive decay is a statistical process. Radioactivity is independent of all external conditions The number of decays per unit time or decay rate is called activity. Activity exponentially decreases with time. Mean lifetime is always greater than half-life time.**

**Choose the correct statement about radioactivity:**

Solution

(d)
Radioactivity is independent of all external conditions. When a nucleus undergoes an Î±-decay, its atomic number decreases by 2 and in beta decay, atomic number increases by 1