Atoms and Nuclei Soved Problems

University:
Minnesota State University Moorhead
Course:
CHEM-150 | General Chemistry I
Academic year:

2023
Views:

301

Pages:

2
Author:

Andreas Barnett

ATOMS AND NUCLEI SOLVED PROBLEMS 1. In a radioactive decay as follows 0  1 e A   A 1  A2 The mass number and atomic number of A2 are 176 and 71 respectively, what are the mass numbers and atomic numbers of A1 and A. Which of these elements are isobars. Sol. The reaction may be expressed as z X A  z 1 Y A  1 e 0  z  3 Y1A  4  2 He 4 (A) (A1 ) (A 2 ) Give Z – 3 = 71  Z = 74 and Z – 1 = 73 Also A – 4 = 176  A = 180 Thus mass number of A1 and A are 180 each The atomic numbers of A1 and A are 73 and 74 respectively. The elements A and A1 are isobars. 2. A radioactive nucleus A undergoes a series of decay according to following scheme :      A  A 1  A 2  A 3  A4 The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A4. Sol. The decay scheme may completely be represented as  72     176 176 172 172 A 180     70 A 1 71 A 69 A 3 69 A 4 Clearly, mass number of A4 is 172 and atomic number is 69. 3. A radioactive isotope D decays according to sequence 1  0n D   D1  D2 If the mass number of atomic number of D2 are 176 and 71 respectively, find the mass number and atomic number of D. Amongst D, D1 and D2 do we have any isobars or isotopes ? Sol. The decay scheme may be represented as 1 z 0n D A   Z D1 A 1 Given Z – 2 = 71 and A – 5 = 176   A 5  Z2 D2 Z = 73 and A = 181 The mass number of D is 181 and atomic number 73. Clearly D and D1 are isotopes. 4. Draw a graph showing the variation of potential energy between a pair of nucleons as a function of their separation. Indicate the regions in which the mnucleus force is (i) attractive, (ii) repulsive. ATOMS AND NUCLEI Sol. Part AB represents repulsive force and Part BCD represents attractive force. A +100 Repulsive B MV0 –100 Attractive 1 2 3 4 r (fm) 5. Sol. Define the term : Half-life period and decay constant of a radioactive sample. Derive the relation between these terms. Half-life Period : The half-life period of an element is defined as the time in which the number of radioactive nuclei decay to half of its initial value. Decay Constant : The decay constant of a radioactive element is defined as the reciprocal of time in which the number of undecayed nuclei of that radioactive element falls to 1 times e of its initial value. Relation between Half-life and Decay Constant : The radioactive decay equation is N = N0 e– t ...(1) when t = T, N = N0 2 N0  N0 e  t 2 or e  t  1 2 ...(2) Taking log of both sides – T loge e  loge 1  loge 2 or T  loge 2 T=  loge 2 λ ...(3) 2.3026 log10 2 2.3026  0.3010    or T= 0.6931 