Atoms and Nuclei Exercise - I

ATOMS AND NUCLEI EXERCISE - I UNSOLVED PROBLEMS 1. What is the shortest wavelength present in the Paschen series of spectral lines ? 2. The ground sate energy of hydrogen atom is – 13.6 eV. What are the KE and PE of the electron in this state ? 3. A hydrogen atom initially in the ground lvel absorbs a photon, which exictes it to the n= 4 level. Determine the frequency and wavelength of photon. 4. The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11 m. What are the radii of n = 2 and n = 3 orbits ? 5. The total energy of an electron in the first excited state of the hydrogen atom is about – 3.4 eV (a) What is the KE of the electron in this state ? (b) What is the PE of the electron in this state ? (c) Which of the answers would change if the zero of PE is change ? 6. Half life of a certain radioactive mateial is 100 days. After how much time the undecayed fraction will be 6.25 % 7. A radioactive material is reduced to 1/16 of its original amount in 4 days. How much material should one begin with so that 4 × 10–3 kg of the material is left after 6 days ? 8. Write the equation for (i) - decay of (ii) + decay of 6C11 9. (iii) – decay of Ra226 88 P32 15 Two different radioactive elements with half lives T1 and T2 have N1 and N2 undecayed atoms respectively present at a given instant. Determine the ratio of their activities at this instant. 10.   The radioactive isotope D decays according to the sequence D  D1  D 2 . If the mass number and atomic number of D2 aer 176 and 71 respectively, what is (i) the mass number (ii) atomic number of D ? 11. With the help of an example, explain how the neutron to proton ratio changes during a decay of a nucleus ? 12. Calculate the energy required by an electron to jump from the ground state to the second excited state ? 13. A radioactive sample decays to 1/32 of its initial activity in 25 days. Calcualte the half life of the substance. 14. The half life of C is 5700 years. What does it mean ? Two radioactive nuclei X and Y initially 14 contain an equal number of atom. Their half life is 1 hour and 2 hours respectively. Calculate the ratio of their rates of disintegration after 2 hours. [one half of the present number of radioactive nucei will remain undecayed after 5700 years] ATOMS AND NUCLEI 15. Calculate the BE per nucleon of Ca40 nucleus. Given m(20Ca40) = 39.962589 u, mass of 20 neutron = 1.008665 u, mass of proton = 1.007825 u 16. If the nucleons of a nucleus are separated for apart from each other, the sum of masses of all the nucleons is larger than the mass of the nucleus. Where does this mass difference come from ? Calculate the energy released if 238U nucleus emits an -particle. Given atomic mass of U = 238.0508 u, atomic mass of 238 234 Th = 234.04363 u, atomic mass of alpha-particle = 4.00260 u and 1u = 931 MeV/e2. 17. What is the effect on neutron to proton ratio in a nucleus when (i) an electron (ii) a positron is emitted ? [In emission of an electron, a neutron is converted into a proton. Therefore, number of neutrons decreases and the number of proton increases. The neutron to proton ratio decrease. In the emission of a positron, a proton is converted into a neutron. Hence the ratio increases. 18. Which one of 3 X 7 and 3 Y 4 is likely to be more stable ? Give reason. [ 3 X 7 is likely to be more stable as it contains larger number of neutrons (4) as compared to 3 19. Y 4 , which contains only one neutron. The half life of 38 Sr 90 is 28 years. What is the disintegration rate of 15 mg of this isotope ? ATOMS AND NUCLEI ANSWER KEY EXERCISE - I UNSOLVED PROBLEMS 1. [R/9 = 8199 Å] 2. [KE = 13.6 eV, PE = –27.2 eV] 3. [3.078 × 1015 Hz, 974.4 Å] 4. [2.12 × 10–10 m, 4.77 × 10–10 m] 5. (a) [3.4 eV], (b) [–6.8 eV], (c) [PE] 6. [400 days] 8. (i) [ 88 Ra 226 86 Rn232  2 He 4 ] , (ii) [ 6 C11  5 B11  e   ] , 7. [0.256 kg] (iii) [15 P 32 16 S 32  e –   ] 9.  N1T2     N2 T1  10. [180, 72] 12. [12.09 eV] 13. 14. [one half of the present number of radioactive nucei will remain 11. [5 days] undecayed after 5700 years] 15. [8.55 MeV] 19. [More] [7.87 × 1010 Bq]