Q.1. A nucleus with mass number 240 breaks into fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is: (2021)
A: 804 MeV
B: 216 MeV
C: 0.9 MeV
D: 9.4 MeV
Ans: B
Solution:
Given binding energy per nucleon of X, Y & Z are 7.6 MeV, 8.5 MeV & 8.5 MeV respectively.
Gain in binding energy is :
Q = Binding Energy of products – Binding energy of reactants
= (120 × 8.5 × 2) – (240 × 7.6) MeV
= 216 MeV
Q.2. A radioactive nucleus undergoes spontaneous decay in the sequence
Where Z is the atomic number of element X. The possible decay particles in the sequence are : (2021)
A: β^{+},α,β^{}
B: β^{},α,β^{+}
C: α,β^{},β^{+}
D: α,β^{+},β^{}
Ans: A
Solution:
β^{+} decreases atomic number by 1
α decreases atomic number by 2
β^{} decreases atomic number by 1
Q.3. The halflife of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be: (2021)
A: 2/3
B: 2/3√2
C: 1/2
D: 1/2√2
Ans: D
Solution:
Q.4. The energy equivalent of 0.5 g of a substance is : (2020)
A: 1.5×10^{13} J
B: 0.5×10^{13}J
C: 4.5×10^{16}J
D: 4.5×10^{13}J
Ans: D
Solution:
E = Δmc^{2} = 0.5 × 10^{3} × (3 × 10^{8})^{2}
= 0.5 ×10^{3} × 9 ×10^{16}
E = 4.5 ×10^{13} J
Q.5. When a uranium isotopeis bombarded with a neutron, it generates three neutrons and : (2020)
A:
B:
C:
D:
Ans: C
Solution:
92 = 36 + Z; ← A + 89 + 3 = 235 ⇒ A = 144
Z = 56
Q.6. For a radioactive material, halflife is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is: (2018)
A: 20
B: 10
C: 30
D: 15
Ans: A
Solution:
Q.7. Radioactive material 'A' has decay constant '8 λ' 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? (2017)
A: 1/7λ
B: 1/8λ
C: 1/9λ
D: 1/10λ
Ans: A
Solution:
Q.8. The Binding energy per nucleon of nuclei are 5.60 MeV and 7.06 MeV, respectively. In the nuclear reaction the value of energy Q released is : (2014)
A: 8.4 MeV
B: 17.3 MeV
C: 19.6 MeV
D: −2.4 MeV
Ans: B
Solution:
Q.9. A radio isotope ‘X’ with a half life 1.4 × 10^{9} years decays to ‘Y’ which is stable. A sample of the rock from a cave was found to contain ‘X’ and ‘Y’ in the ratio 1 : 7. The age of the rock is (2014)
A: 4.20 × 10^{9} years
B: 8.40 × 10^{9} years
C: 1.96 × 10^{9} years
D: 3.92 × 10^{9} years
Ans: A
Solution:
Ratio of X:Y is given = 1:7
That is,
⇒ 7m_{x} = m_{y}
Let, the initial total mass is m.
Therefore, time taken to become 1/8 unstable part
= 3 x T_{1/2}
= 3 x 1.4 x 10^{9}
= 4.2 x 10^{9} y
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