Question 31:
easyThe mass of a proton is \(1.0073\text{ u}\) and that of neutron is \(1.0087\text{ u}\) (\(u = \text{atomic mass unit}\)). The binding energy of \({}_2\text{He}^4\) is (mass of helium nucleus = \(4.0015\text{ u}\))
Mass defect \(\Delta m = (2 m_p + 2 m_n) - m_{\text{He}} = [2(1.0073) + 2(1.0087)] - 4.0015 = 0.0305\text{ u}\). Binding energy is \(E_b = \Delta m \times 931.5\text{ MeV} \approx 0.0305 \times 931.5 \approx 28.4\text{ MeV}\).
Question 32:
easyBeta positive decay is
In \( \beta^+ \) decay, a proton inside the nucleus converts into a neutron, emitting a positron (\( e^+ \)) and a neutrino (\( \nu_e \)). The nuclear reaction is \( p \rightarrow n + e^+ + \nu_e \).
Question 33:
easyIf \( E \) is the energy of \( n^{\text{th}} \) orbit of hydrogen atom, the energy of \( n^{\text{th}} \) orbit of \( \text{He}^+ \) ion will be
The energy of an electron in a hydrogen-like atom is given by \( E_n \propto Z^2 \). For hydrogen, \( Z = 1 \), and for helium ion \( \text{He}^+ \), \( Z = 2 \). Therefore, \( E_{\text{He}^+} = Z^2 E = 4E \).
Question 34:
easyIf the radius of a nucleus of mass number 2 is R, then radius of a nucleus of mass number 16 is
The radius of a nucleus is given by \(R \propto A^{1/3}\). Therefore, \(frac{R'}{R} = \left(\frac{16}{2}\right)^{1/3} = 8^{1/3} = 2\), so \(R' = 2R\).
Question 35:
easyChoose the incorrect statement among the following.
Nuclides with the same atomic number \(Z\) but different neutron number \(N\) are called isotopes. Isotones are nuclides with the same number of neutrons.
Question 36:
easySurface area of the nucleus (\(X^8\)) is \(A_0\), then surface area of nucleus (\(Y^{64}\) ) will be
Nuclear radius is given by \(R \propto A^{1/3}\), so the surface area is \(S \propto R^2 \propto A^{2/3}\). Thus, \(\frac{S_2}{S_1} = \left(\frac{64}{8}\right)^{2/3} = 8^{2/3} = 4\), meaning the surface area of the nucleus \(Y^{64}\) is \(4A_0\).
Question 37:
easyChoose the incorrect statement among the following.
Nuclides with the same atomic number \( Z \) but different neutron numbers \( N \) are called isotopes, not isotones. Thus, option C is incorrect.
Question 38:
easyAssertion (A): An electron and a positron moving towards each other with equal and opposite velocities can annihilate into photons.
Reason (R): A photon has non zero energy and momentum.
Electron-positron annihilation converts their mass-energy into radiant energy, typically two gamma-ray photons to conserve momentum. Photons indeed possess non-zero energy and momentum. However, the reason describes a property of the resulting photons rather than the fundamental cause or mechanism of the annihilation process itself.
Question 39:
easyAssertion (A): For the scattering of \(\alpha\)-particles at a large angles only the nucleus of the atom is responsible.
Reason (R): Nucleus is very heavy in comparison to electrons.
In Rutherford's alpha-scattering experiment, large-angle deflections are caused by the strong electrostatic repulsion from the positively charged, massive nucleus. Electrons, being much lighter, cause negligible deflection. The nucleus's significant mass (R) ensures it remains largely stationary during collision, allowing for large deflections of \(\alpha\)-particles (A).
Question 40:
easyAssertion (A): A beam of charged particles is employed in the treatment of cancer.
Reason (R): Charged particles on passing through a material medium lose their energy by causing ionization of the atoms along their path.
Assertion (A) is true; charged particle therapy (e.g., proton therapy) is used for cancer. Reason (R) is true; charged particles lose energy mainly through ionization, creating a Bragg peak that can precisely damage tumor cells. (R) is the correct explanation for (A).