Composition and size of nucleus, atomic masses
- ^290_82X α Y e^+ Z β^- P e^- QIn the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are : Answer: 1. 286, 81 Key idea: α emission lowers A by 4 and Z by 2; β^+ (positron) lowers Z by 1; β^- (electron) raises Z by 1. The mass numbe... 1
- The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to ≤ft(1/16)^th of its initial value? Answer: 1. 80 minutes Activity falls by half every half-life. dfrac116=(1/2)⁴ , so 4 half-lives are needed. t=4×20=80 minutes. The answer is... 1
- A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is : Answer: 4. 5 : 4 Nuclear radius is R=R₀A^(1/3) . R₁/R₂=(125/64)^(1/3)=5/4 The ratio is 5:4 . Option (4). 1
- In the given nuclear reaction, the element X is :^22_11Na → X + e^+ + Answer: 4. ²²₁₀Ne The emission of a positron is beta-plus decay: a proton turns into a neutron, so the mass number stays the same and the at... 1
- A radioactive nucleus ^A_ZX undergoes spontaneous decay in the sequence^A_ZX → _Z-1B → _Z-3C → _Z-2D, where Z is the atomic number of element X. The possible decay particles in the sequence are : Answer: 3. β^+, α, β^- Key idea: α decay lowers Z by 2; β^- raises Z by 1; β^+ lowers Z by 1. Z→ Z-1 : β^+ . Z-1→ Z-3 : α . Z-3→ Z-2 : β^- .... 1
- The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be : Answer: 2. 1/2√(2) Key idea: activity decays as A=A₀(1/2)^t/T_(1/2) . dfrac AA₀=(1/2)^(150/100)=(1/2)^(3/2)=dfrac12sqrt2 . Option 2. 1
- α-particle consists of : Answer: 1. 2 protons and 2 neutrons only An α -particle is the nucleus of a helium atom, ⁴₂He : 2 protons and 2 neutrons, with no electrons. 1
- 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 Answer: 1. 20 If 450 of 600 nuclei disintegrate, 150 remain, which is 1/4 of the original. N/N₀=(1/2)ⁿ=1/4⇒ n=2 half-lives. Time =2×10=20 mi... 1
- Radioactive material 'A' has decay constant '8λ' and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be 1/e ? Answer: 1. 1/7λ Key idea: N=N₀e^(-λ t) for each material, and take the ratio of the two. N_A=N₀e^(-8λ t) , N_B=N₀e^(-λ t) . Then N_A/N_B=e^(... 1
- 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 Answer: 3. 60 Use N=N₀(1/2)^(t/T) and compare the remaining fractions. 40% decayed means 60% remains; 85% decayed means 15% remains. Ratio o... 1