Atoms

33 solved questions from Class 12 Physics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the fundamental law or governing principle of 'Atoms' in Class 12 Physics? medium MCQ Fundamental Physical Law
• 2 What is the SI unit and dimensional formula for the key physical quantity studied in 'Atoms'? medium MCQ SI Units & Dimensional Analysis
• 3 How does the field or potential intensity vary with distance r in 'Atoms'? medium MCQ Spatial Distance Dependence
• 4 What is the net flux or circulation integral through a closed surface in 'Atoms'? medium MCQ Gauss's Theorem & Boundary Integrals
• 5 Why do field lines in 'Atoms' never intersect each other? medium MCQ Field Line Properties
• 6 A hydrogen‑like ion has nuclear charge Z = 3 (e.g., Li^2+). Using the Bohr model, the energy of the electron in the n^th orbit is E_n = -13.6 Z^2/n^2 eV. What is the energy of the electron when it is in the n=2 orbit? medium 3 marks Energy levels of hydrogen-like ions in Bohr model
• 7 For an electron in the ground state of a hydrogen atom, what are the values of the orbital quantum number l and the magnetic quantum number m_l? medium 3 marks Quantum numbers for hydrogen ground state
• 8 In the Rutherford atomic model, the electric field intensity produced by the nucleus at a distance r from the nucleus is expressed in SI units. Which of the following is the correct SI unit for electric field intensity? easy MCQ 1 mark SI unit of electric field in atomic context
• 9 An electron is confined in a cubic region of length L = 1.0 × 10^-10 m. Using Heisenberg’s uncertainty principle Δ x Δ p ≥ ħ/2, estimate the minimum kinetic energy of the electron. Take m_e = 9.11 × 10^-31 kg and ħ = 1.055 × 10^-34 J·s. Express your answer in electron‑volts. hard 4 marks Heisenberg uncertainty principle applied to electrons in atoms
• 10 Using the Schrödinger equation for the hydrogen atom, the ground‑state energy is E_1=-(m_e e^4)/(8ε_0^2 h^2). Given m_e=9.11×10^-31,kg, e=1.602×10^-19,C, ε_0=8.854×10^-12,C^2!!/!N·m^2, and h=6.626×10^-34,J·s, calculate E_1 in electron‑volts. hard 4 marks Schrödinger ground‑state energy
• 11 A hydrogen‑like ion has nuclear charge Z=2 (e.g., Δ^+). Using the Bohr formula E_n=-13.6,Z^2/n^2 eV, calculate the energy difference Δ E needed to excite an electron from the ground state (n=1) to the n=3 orbit. medium 2 marks Bohr energy levels
• 12 An electron has intrinsic spin angular momentum S=hbar/2. The magnetic moment due to spin is mu_s = g_s,ehbar/2m_e,S/hbar where g_ssimeq2. Compute the value of mu_s in units of Bohr magneton mu_B=ehbar/2m_e. hard 3 marks Electron spin magnetic moment
• 13 A particle of mass m_e is confined in a cubic box of side L=0.5,nm. Using the particle‑in‑a‑box model, compute the ground state energy E_1 of the electron and give the result in electron‑volts. Use h=6.626×10^-34,J·s and m_e=9.11×10^-31,kg. hard 4 marks Quantum confinement in 3D box
• 14 An electron is confined in a one‑dimensional box of length L=0.5,nm. Using the uncertainty principle Δ x,Δ pgehbar/2, estimate the minimum kinetic energy K of the electron. Take m_e=9.11×10^-31,kg and ħ=1.055×10^-34,J·s. Express K in electron‑volts. hard 3 marks Heisenberg uncertainty in confined systems
• 15 A hydrogen‑like ion with nuclear charge Z=4 is in the ground state. Using the Bohr formula E_n = -13.6,Z^2/n^2 eV, what is the energy difference Δ E required to excite the electron from n=1 to n=2? easy MCQ 1 mark Bohr model energy levels
• 16 An electron has intrinsic spin angular momentum S=ħ/2. The spin magnetic moment is μ_s = -g_s e/2m_eS. Given g_s=2.0023, calculate |μ_s| in units of the Bohr magneton μ_B = ehbar/2m_e. medium 2 marks Spin magnetic moment
• 17 An electron has intrinsic spin angular momentum S= hbar/2. The spin magnetic moment is mu_s=-g_s e/2m_eS. Given g_s=2.0023, what is |mu_s| in units of the Bohr magneton mu_B= ehbar/2m_e? easy MCQ 1 mark Spin magnetic moment in Bohr magneton
• 18 Explain how the Bohr radius of a hydrogen‑like ion changes when the nuclear charge Z is increased from 1 to 2 or 3. Include the formula and the physical reasoning. hard 3 marks Bohr radius dependence on nuclear charge
• 19 A one‑dimensional box of length L=0.3 nm contains an electron. Using the particle‑in‑a‑box model, calculate the ground state energy E_1 in electron‑volts. Use h=6.626×10^-34 J·s and m_e=9.11×10^-31 kg. medium 2 marks Particle‑in‑a‑box ground state energy
• 20 An electron is confined in a cubic box of side L=1.0 nm. Using the uncertainty principle Δ x,Δ pgeħ/2, estimate the minimum kinetic energy K of the electron. Take m_e=9.11×10^-31 kg and ħ=1.055×10^-34 J·s. Express K in electron‑volts. medium 2 marks Uncertainty principle minimum kinetic energy
• 21 An electron is accelerated through a potential difference of 150 V. Assuming it starts from rest, calculate the de Broglie wavelength of the electron in nanometres. Use h = 6.626×10^-34 J·s, m_e=9.11×10^-31 kg and e=1.602×10^-19 C. easy 1 mark de Broglie wavelength
• 22 A hydrogen‑like ion with nuclear charge Z=5 (boron^4+) is in its ground state (n=1).\ hard 4 marks Energy levels of hydrogen‑like ions
• 23 For an electron in the ground state of a hydrogen atom, which set of quantum numbers is correct? medium MCQ 2 marks quantum numbers of hydrogen ground state
• 24 Calculate the radius of the third Bohr orbit (n=3) of a Li^2+ ion (nuclear charge Z=3). Use the Bohr radius a_0=0.529 Å. medium 3 marks Bohr radius for hydrogen‑like ions
• 25 An electron is accelerated from rest through a potential difference of 300 V. (i) Find its de Broglie wavelength in picometres. (ii) The same electron is confined in a one‑dimensional box of length L = 0.4 nm. Calculate the wavelength of the photon emitted when the electron makes a transition from the first excited state (n = 2) to the ground state (n = 1). Assume the photon energy equals the difference of the box energy levels. Give the wavelength in nanometres. Use h = 6.626×10⁻³⁴ J·s, mₑ = 9.11×10⁻³¹ kg, e = 1.602×10⁻¹⁹ C, and c = 3.00×10⁸ m/s. hard 5 marks de Broglie wavelength and particle‑in‑a‑box transitions
• 26 What is the correct set of quantum numbers (n, l, m_l, m_s) for the only electron in the ground state of a He⁺ ion? easy MCQ 1 mark Quantum numbers for hydrogen‑like ground state
• 27 Calculate the radius of the fourth Bohr orbit (n = 4) of a Be³⁺ ion (nuclear charge Z = 4). Use the Bohr radius a₀ = 0.529 Å. medium 2 marks Bohr radius for hydrogen‑like ions
• 28 Calculate the magnitude of the electron spin magnetic moment in units of the Bohr magneton μ_B, given the electron g‑factor g_s = 2.0023. medium 2 marks Spin magnetic moment of electron
• 29 An electron is confined in a one‑dimensional box of length L=0.6 nm. Using the particle‑in‑a‑box model, the electron makes a transition from the n=3 level to the n=1 level. Calculate the wavelength of the emitted photon in nanometres. (Use h=6.626×10^-34 J·s, m_e=9.11×10^-31 kg, c=3.00×10^8 m/s.) hard 4 marks Particle in a box transition wavelength
• 30 For the hydrogen‑like ion He⁺ (nuclear charge Z=2), which set of quantum numbers (n, l, m_l, m_s) correctly describes its only electron in the ground state? easy MCQ 1 mark Quantum numbers for hydrogen‑like ion
• 31 A hydrogen‑like ion Li^2+ (Z=3) and Be^3+ (Z=4) are considered. (i) Write the expression for the radius r_n of the n^th Bohr orbit for a hydrogen‑like ion. (ii) Calculate the radius of the n=3 orbit for Li^2+. (iii) Calculate the radius of the n=4 orbit for Be^3+. (iv) Find the ratio r_3(Li^2+)/r_4(Be^3+). (Use a_0=0.529 Å.) hard 5 marks Bohr radii of hydrogen‑like ions
• 32 An electron is accelerated from rest through a potential difference of 250 V. Calculate its de Broglie wavelength in picometres. (Use h=6.626×10^-34 J·s, m_e=9.11×10^-31 kg, e=1.602×10^-19 C.) medium 2 marks de Broglie wavelength of accelerated electron
• 33 For a helium ion He⁺ (nuclear charge Z=2), find the radius of the third Bohr orbit (n=3). Use the Bohr radius a_0 = 0.529,Å. medium 3 marks Bohr radius scaling with nuclear charge