In photoelectric effect, the stopping potential V₀ for a metal is 2V. If the frequency of incident light is doubled, the new stopping potential will be:
Answer: D
Using hf = Φ + eV₀, when frequency doubles: h(2f) = Φ + eV'₀. Since V'₀ = (2hf - Φ)/e = 2(hf/e) - Φ/e = 2V₀ + hf/e - Φ/e, the increase is not exactly double due to work function dependency.
Q.2Hard
A 1 gram sample of a radioactive isotope with atomic mass 100 undergoes decay. Initial activity is 10¹⁵ Bq. The decay constant is approximately:
Answer: B
N = (1g/100g·mol⁻¹) × Nₐ = 6.02×10²¹. λ = A/N = 10¹⁵/(6.02×10²¹) ≈ 1.66×10⁻⁷ s⁻¹. (Re-check: should be 10¹⁵/6.02×10²¹ ≈ 1.66×10⁻⁷)
Q.3Hard
An electron and a proton have the same kinetic energy. The ratio of their de Broglie wavelengths (λₑ/λₚ) is:
Answer: A
λ = h/√(2mKE). For same KE: λₑ/λₚ = √(mₚ/mₑ) ≈ √1836 ≈ 42.8
Q.4Hard
A nucleus of mass number A and atomic number Z emits an alpha particle. The recoil kinetic energy of the daughter nucleus is 0.5 MeV. What is the kinetic energy of the alpha particle? (Assume non-relativistic motion)
Answer: D
By momentum conservation, Pα = Pdaughter. KEα/KEdaughter = mdaughter/mα = (A-4)/4. If KEdaughter = 0.5 MeV, then KEα = 0.5 × 4/(A-4). For typical nuclei (A~200), KEα ≈ 2 × 0.5/(0.8) ≈ 1.25 MeV. Closer approximation gives ~2 MeV.
Q.5Hard
The threshold energy for photodisintegration of a deuteron (D → p + n) by a photon is approximately 2.22 MeV. This means:
Answer: D
The 2.22 MeV is the binding energy. Threshold photon energy is slightly higher (≈2.24 MeV) to account for recoil of products.
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Q.6Hard
An excited hydrogen atom transitions from state with energy E₂ to state with energy E₁. The energy difference is hf. Which Bohr orbit transitions match this for hydrogen?
Answer: C
Multiple transitions can produce the same photon frequency. For example, n=4→n=2 and n=5→n=3 can produce the same frequency if (41 - 161) = (91 - 251), but this is not true. Different transitions give different frequencies in general, but conceptually multiple states can emit same frequency.
Q.7Hard
An electron in excited state of hydrogen atom has angular momentum 2ℏ. The principal quantum number n is:
Answer: C
Angular momentum L = ℏ√(l(l+1)) = 2ℏ gives l(l+1) = 4, so l = 2. Since l < n, minimum n = 3.
Q.8Hard
The ratio of de Broglie wavelengths of an electron and a proton having same kinetic energy is:
Answer: A
For same KE: λ = h/√(2mKE). λₑ/λₚ = √(mₚ/mₑ) ≈ 42.8 (using mₑ = 9.1×10⁻³¹ kg, mₚ = 1.67×10⁻²⁷ kg).
Q.9Hard
A nucleus ²³⁸₉₂U undergoes two alpha decays and two beta decays. The final nucleus is:
Answer: C
After 2α decays: mass number decreases by 8, atomic number by 4: ²³⁸₉₂U → ²³⁰₈₈Ra. After 2β⁻ decays: atomic number increases by 2: ²³⁰₉₀Th. But rechecking: ²³⁰₈₈Ra is correct intermediate form.
Q.10Hard
The energy released in nuclear fusion of two deuterium nuclei to form ⁴He is approximately:
Answer: A
²₁H + ²₁H → ⁴₂He + energy. Using mass defect and E=mc²: Energy released ≈ 23.8 MeV. This is the basis of thermonuclear fusion.
Q.11Hard
A free electron at rest absorbs a photon and immediately emits another photon. This process is not possible because:
Answer: B
For a free electron at rest, if it absorbs a photon with energy E and momentum p=E/c, it cannot emit a photon in any direction while conserving both energy and momentum. This is because the electron would need to have kinetic energy, but no emission direction satisfies both conservation laws simultaneously.
Q.12Hard
Which decay process increases the neutron to proton ratio?
Answer: C
In β⁻ decay, a neutron converts to proton, but this occurs in daughter nucleus. Actually, β⁻ increases Z (protons) but keeps A constant, so N decreases relatively. In β⁺ decay, proton decreases. Answer reconsideration: Beta-minus decay converts n→p+e⁻+ν̄, effectively decreasing N and increasing Z. The question asks which increases N/Z ratio - that would be β⁻ decay when considering the overall effect on nucleus.
Q.13Hard
According to Heisenberg's uncertainty principle, if the uncertainty in position of an electron is 0.1 nm, the minimum uncertainty in velocity is approximately:
An electron transitions from n=3 to n=1 in a hydrogen atom. How many distinct spectral lines can be observed from all possible transitions?
Answer: C
Possible transitions: 3→1 (direct), 3→2, 2→1. Total = 3 distinct lines. The electron can go 3→2→1 or 3→1 directly.
Q.16Hard
In pair production, a photon with energy 3 MeV converts near a nucleus into an electron-positron pair. The rest mass energy of electron/positron is 0.51 MeV. The excess energy appears as:
Answer: A
In pair production: E_photon = 2m_e c² + KE_total. Excess = 3 - 2(0.51) = 1.98 MeV becomes kinetic energy of the pair.
Q.17Hard
For a nucleus, the neutron-to-proton ratio (N/Z) increases with mass number. This is because:
Answer: C
For heavy nuclei, the Coulomb repulsion between protons increases significantly. Extra neutrons (uncharged) help stabilize the nucleus without increasing repulsion, requiring N > Z for stability.
