Nuclei-Quiz-1

 

NUCLEI QUIZ-1

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.

Q1The radioactivity of a sample is R_1 at a time T_1 and R_2 at a time T_2. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T_2-T_1) is proportional to

•  R1 T1=R2 T2 ²
•   R1-R2 ²
•   ((R1-R2))/T d) ²
•   (R1-R2 )T ²

Solution

Q2.  The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both them have the same number of atoms. Then ^xk^y, where C is a dimensionless constant. The values of x and y are, respectively

•   X and Y have the same decay rate initially
•  - X and Y decay at the same rate always
•   Y will decay at a faster rate than X
•  - X will decay at a faster rate than Y

Solution

 

Q3.  Consider the following reaction ^1 H_2+ ^1 H_2→ _( 1) He^4+Q If m(_1 H^2)=2.0141 u;m(_2 He^4)=4.0024 u, the energy Q released (in MeV) in this fusion reaction is

•   12
•  6
•  24
•  48

Solution

Q4. Which of the following is a correct statement?

•   Beta rays are same as cathode rays
•   Gamma rays are high-energy neutrons
•  Alpha particles are singly ionized helium atoms
•   Protons and neutrons have exactly the same mass

Solution
(a) Both the beta rays and the cathode rays are made up of electrons. So, only option (a) is correct Gamma rays are electromagnetic waves Alpha particles are doubly ionized helium atoms Protons and neutrons have approximately the same mass Therefore, (b), (c) and (d) are wrong options

Q5.  90% of a radioactive sample is left undecayed after time t has elapsed. What percentage of the initial sample will decay in a total time 2t?;">

•  20%
•  19%
•  40%
•  38%

Solution
 5 (b) 90% of the sample is left undecayed after time t ∴9/10 N_0=N_0 e^(-λt) λ=1/t ln⁡(10/9) (i) After time 2t, N_c=N_0 e^(-λ(2t) )=N_0 e^(-1/t [ln⁡(10/9) ]2t) (ii) N=N_0 e^〖-ln〗⁡〖(10/9)^2 〗 =N_0 (9/10)^2≈81% of N_0 (iii) Therefore, 19% of initial value will decay in time 2t

Q6. A physical quantity X is represented by X=(M^xL^-yT^-z). Binding energy per nucleon verses mass number curve for nuclei is shown in the figure. W,X,Y and Z are four nuclei indicated on the curve. The process that would release energy is

 

• Y→2Z
• W→X+Z
  
• W→2Y
  
•  X→Y+Z

Solution

6 (c) Energy is released in a process when total binding energy (B.E.) of the nucleus is increased or we can say when total B.E. of products is more than the reactants. By calculation we can see that only in case of option (c), this happens Given W→2Y B.E. of reactants =120×7.5=900 MeV and B.E. of products =2×(60×8.5)=1020 MeV i.e.,B.E. of products > B.E. of reactants

Q7.  The binding energies of nuclei X and Y are E_1 and E_2, respectively. Two atoms of X fuse to give one atom of Y and an energy Q is released. Then,

•   Q=2E1-E2
•   Q=E2-〖2E1)]
•   Q< 2E1-E2<2e_1-e_2 span="">
•   Q>E2-〖2E1)]

Solution
7(b) During fusion, binding energy of daughter nucleus is always greater than the total binding energy of the parent nuclei. The difference of binding energies is released. Hence, Q=E2-〖2E〗_1

Q8. A radioactive sample of U^238 decays to Pb through a process for which half life is 4.5×10^9 years. The ratio of number of nuclei of Pb to U^238 after a time of 1.5×10^9 years (given 2^(1/3)=1.26)

•  0.12
•  0.26
•  1.2
•  0.37

Solution

 

Q9.  What is the power output of _92^ U^235 reactor if it takes 30 days to use up 2 kg of fuel and if each fission gives 185 MeV of usable energy? Avogadro’s number =6.02×10^26 per kilomole 

•  45 megawatt
•  58.46 megawatt
•  72 megawatt
•  92 megawatt

Solution

Q10.In hydrogen spectrum, the wavelength of Hα line is 656 nm, whereas in the spectrum of a distant galaxy, Hα line wavelength is 706 nm. Estimated speed of the galaxy with respect to earth is

•  2×10^8 m s^(-1)
•   2×10^7 m s^(-1)
• 2×10^6 m〖 s〗^(-1)
• 2×10^5 m s^(-1)
  
  

Solution