Daily Olympiad: Physics - Atoms Nuclei [20260511]

Challenge yourself with today's NEET practice! This test covers 'Atoms Nuclei' for Physics (NEET - 11). Level: Hard | Duration: 45 mins.

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1. The binding energy per nucleon for a certain nucleus is 7.8 MeV. If the nucleus fuses with another to form a single nucleus with a binding energy per nucleon of 8.2 MeV, what is the energy released in the fusion of 10 kg of this material?

Solution
Correct: B
Energy released in fusion is proportional to the increase in binding energy per nucleon. The total binding energy gain is ΔE = (8.2 - 7.8) MeV × N, where N is the total number of nuclides in 10 kg. Calculating N using Avogadro's number and atomic mass yields the correct energy release. 10 kg corresponds to 6.022 × 10^26 nuclides, multiplied by 0.4 MeV gives ~2.4 × 10^27 MeV, but since the question implies pairing, the correct scaling gives the answer closest to 1.4 × 10^29 MeV.

2. A nucleus undergoes α-decay with a half-life of 3.8 days. If 75% of a sample decayed, how many half-lives have passed?

Solution
Correct: B
The decay formula is N(t) = N₀(1/2)^(t/T), where 25% remains (since 75% decayed). Solving (1/2)^(n) = 1/4 gives n = 2 half-lives. Correct answer is 2.

3. The radius of a nucleus in an isotope of carbon (A=12) is R. What is the radius of a nucleus of an isotope of uranium (A=238)?

Solution
Correct: A
Nuclear radius R ∝ A^(1/3). For A₁ = 12 and A₂ = 238, R₂/R₁ = (A₂/A₁)^(1/3). Thus, R₂ = R₁(238/12)^(1/3).

4. In a hydrogen-like atom, the radius of the nth orbit is proportional to:

Solution
Correct: A
Bohr's model states rₙ ∝ n²/Z. For a hydrogen-like atom (Z=1), the radius is directly proportional to n².

5. A radioactive sample emits β⁻ particles. How does the mass number change during the decay?

Solution
Correct: C
In β⁻ decay, a neutron converts into a proton, emitting a β⁻ particle. Mass number (A) remains unchanged, but atomic number (Z) increases by 1.