Class 12 Physics, Chapter 13 (NCERT). 15 questions by concept, 1 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
A neutral helium-4 atom has mass 4.002603u. Each electron has mass 0.000548u. Neglect electronic binding energy. What is the alpha-particle mass?
(b) 4.001507u
An alpha particle is the helium nucleus. Subtract both electron masses: 4.002603-2(0.000548)=4.001507u.
Neglect electronic binding energy. For a neutral atom with Z=2, what is M_atom-M_nucleus in terms of electron mass m_e?
(d) 2m_e
A neutral atom contains Z electrons outside its nucleus. Its mass exceeds the bare nuclear mass by Zm_e to this approximation.
Mercury-198 has Z=80 and gold-197 has Z=79. Which statement correctly classifies this pair?
(b) They are isotones because both have 118 neutrons
Compute 198-80=118 and 197-79=118. Equal neutron number with different proton numbers defines isotones; equal Z is not required.
Which quantity must be equal for two different isotopes of one element?
(a) Number of protons
An element is defined by Z, the proton number. Its isotopes have different neutron numbers and hence different mass numbers.
Why does the empirical law R=R0 A^(1/3) lead to nearly constant nuclear density?
(b) Both nuclear mass and nuclear volume are proportional to A
The volume is (4π/3)R0³A, and the mass is approximately m_nucleon A. Dividing cancels A, giving 3m_nucleon/(4πR0³).
Two nuclei have mass numbers 64 and 125. Using nuclear mass approximately A m_nucleon and R=R0 A^(1/3), what is rho_first:rho_second?
(d) 1:1
Mass and volume both grow in proportion to A, so their ratio is approximately constant. These are nuclear densities, not whole-atom densities.
Free nucleons at rest have combined mass M_free. They form a bound nucleus and release binding energy B. What is the nuclear rest mass?
(a) M_free-B/c²
The released energy reduces the rest energy of the remaining nucleus by B. Its mass is lower by B/c², consistent with positive mass defect.
A parent nucleus initially at rest undergoes an energetically allowed decay X→Y+Z with positive energy release Q. Which rest-mass relation must hold?
(c) M_X>M_Y+M_Z
Positive Q=(M_X-M_Y-M_Z)c² requires the initial rest mass to exceed the sum of final rest masses. The deficit appears as kinetic energy of the products.
On the usual binding-energy-per-nucleon curve, how does the value near iron-56 compare with that for uranium-238?
(d) It is greater near iron-56
The curve reaches its broad maximum near the iron/nickel region and declines for very heavy nuclei. Increasing A does not always increase B/A.
The graph gives nuclear potential energy U as a function of nucleon separation r. What is the radial nuclear force at the marked point P?
(c) Repulsive
At P the potential decreases as separation increases, so dU/dr is negative. Therefore F_r=-dU/dr is positive and pushes the nucleons apart. Binding does not imply attraction at every separation.
The nuclear potential U(r) has a smooth minimum at r=r0. What is the radial nuclear force exactly at r0?
(a) Zero
At a smooth minimum dU/dr=0. The radial force F_r=-dU/dr is therefore zero even though U itself is negative.
In beta-minus decay, how is the emitted electron produced?
(d) It is created when a neutron converts into a proton, with an antineutrino also emitted
Beta-minus conversion is n→p+electron+antineutrino. The emitted electron is created in the process, not a pre-existing nuclear constituent.
What nuclear process supplies the Sun core energy as hydrogen is converted into helium?
(a) Fusion of light nuclei
The proton-proton chain combines light nuclei through several steps whose net result converts hydrogen into helium. This is fusion, rather than splitting heavy nuclei.
In a classical hard-sphere model, two deuterons each have radius 2.0fm and charge +e. With k_e e²=1.44MeV fm, what is the Coulomb energy when they just touch?
(a) 0.36MeV
Their centres are 2.0+2.0=4.0fm apart at contact. The Coulomb energy is 1.44/4.0=0.36MeV. Using one radius would double the result.
A pure plutonium-239 sample has mass 1000g. Use molar mass 239g/mol and Avogadro constant N_A. How many nuclei does it contain?
(a) 1000N_A/239 nuclei
First convert grams to moles by dividing by 239g/mol. Then multiply by N_A to get the number of nuclei. The one-kilogram source case is 1000g.
Wrong
If the first half-life removes an expected 800,000 of 1,600,000 nuclei, the next removes another 800,000.
Why it feels right. The time intervals are equal, so I subtract the same number.
Right
Each half-life halves the expected number remaining.
Worked example
