BPHET-141 Solved Assignment January 2026 | ELEMENTS OF MODERN PHYSICS | IGNOU BSCG

Q: Answer the following questions:

This response addresses a series of questions from BPHET-141, Elements of Modern Physics, covering fundamental concepts such as the photoelectric effect, de Broglie hypothesis, Bragg diffraction, Heisenberg's uncertainty principle, and wave functions. **(a) Photoelectric Effect** The photoelectric effect, a cornerstone of quantum physics, describes the emission of electrons (photoelectrons) when light shines on a material. Einstein's photoelectric equation relates the maximum kinetic energy (K

Q: Answer the following questions:

This response provides a comprehensive analysis of fundamental quantum mechanics problems, drawing upon concepts typically covered in the BPHET-141 course. It addresses the properties of eigenfunctions for a particle in a box, calculates expectation values, derives probability current densities for step potentials, explores the concept of parity in quantum systems, and applies the tunneling probability formula to determine barrier width. Each sub-question is tackled with detailed explanations, s

Q: Answer the following questions:

Nuclear physics deals with the structure, properties, and interactions of atomic nuclei. This includes phenomena like radioactive decay, nuclear reactions such as alpha decay and fusion, and the theoretical understanding of nuclear stability. The semi-empirical mass formula provides a crucial framework for predicting nuclear properties like binding energy and identifying stable isotopes. The following solutions apply these fundamental principles to specific problems.

Q1. Answer the following questions:

(a)) A rod has a proper length of 2.0m. An observer measures its length as 1.6 m. Calculate the speed of the rod. (200 words)
(b)) A spaceship approachin Earth at a speed c/2, shoots a canister at a speed of 0.80c. Calculate the velocity of the canister for an observer on Earth if (i) the canister if it is shot directly toward Earth and (ii) if it is shot directly away from Earth. (200 words)
(c)) A star emits light of wavelength 500 nm and recedes from Earth at speed 0.50c. Calculate the observed wavelength. (200 words)
(d)) A particle moves with speed 0.8c. Calculate its momentum, kinetic energy and total energy. (200 words)
(e)) An electric field of 10º Vm¯¹ is applied along the direction of motion of an electron moving with a speed of 0.6c. Calculate the acceleration of the electron. (200 words)

Key Points:

Length contraction: L = L₀√(1 - v²/c²), observed length L is shorter than proper length L₀ for objects in motion.
Relativistic velocity addition: u = (u' + V) / (1 + u'V/c²), classical velocity addition fails at relativistic speeds.
Relativistic Doppler effect: λ' = λ₀√((1 + v/c) / (1 - v/c)), observed wavelength changes due to relative motion, redshift for receding sources.
Lorentz factor (γ): γ = 1 / √(1 - v²/c²), crucial multiplier for relativistic mass, time, length, momentum, and energy.

Answer: This answer addresses five fundamental problems in Special Relativity, encompassing concepts like length contraction, relativistic velocity addition, relativistic Doppler effect, relativistic energy-momentum relations, and relativistic dynamics (acceleration). Each sub-question demonstrates the application of Einstein's postulates to phenomena involving speeds comparable to the speed of light, where classical Newtonian mechanics and Galilean transformations fail. The solutions involve step-by-st...

Q2. Answer the following questions:

(a)) In a photoelectric effect experiment, it is seen that when light of wavelength 180 nm is incident on a metal, the measured photoelectric current drops to zero at a potential - 1.00 V. Calculate the work function of the metal and its cut-off frequency for photoelectric effect. (200 words)
(b)) Electrons are accelerated through 150V and incident on a crystal with interatomic spacing d = 0.25 nm. Calculate the de Broglie wavelength and the first-order Bragg diffraction angle. (200 words)
(c)) The average decay life time of an elementary particle is 1.0 µs. Calculate the minimum uncertainty in the measurement of its energy. Also, calculate the minimum uncertainty in the measurement of its mass using the mass-energy equivalence. (200 words)
(d)) The normalized wave function for a particle is given by ψ(x) = { 2a√ax eax, x>0 0, x < 0 Determine i) the value of x at which the probability density function is maximum, and iii) the probability of finding the particle between x = 0 and x = 1/a. (400 words)

Key Points:

Photoelectric effect: K_max = E - Φ, where E = hc/λ and Φ = hν₀.
De Broglie wavelength: λ_dB = h / √(2meV) for electrons accelerated by voltage V.
Bragg's Law: 2d sinθ = nλ_dB describes diffraction from crystal planes.
Heisenberg's Energy-Time Uncertainty: ΔE Δt ≥ ħ/2, minimum uncertainty implies equality.

Answer: This response addresses a series of questions from BPHET-141, Elements of Modern Physics, covering fundamental concepts such as the photoelectric effect, de Broglie hypothesis, Bragg diffraction, Heisenberg's uncertainty principle, and wave functions. **(a) Photoelectric Effect** The photoelectric effect, a cornerstone of quantum physics, describes the emission of electrons (photoelectrons) when light shines on a material. Einstein's photoelectric equation relates the maximum kinetic energy (K...

Q3. Answer the following questions:

(a)) The eigenfunction of a particle confined in a box of length L (0 ≤ x ≤ L) is Ψη(x) = VL 2 sin ηπχ L i) Show that wn(x) is not an eigenfunction of the momentum operator. ii) Calculate the expectation value of the kinetic energy. (400 words)
(b)) Calculate the probability current density of the incident and reflected waves for the quantum mechanical particle incident on a step potential V(x) = { 0, x < 0 Vo > 0, x > 0 when E < Vo. (200 words)
(c)) Explain whether the eigen functions of the following Hamiltonian for a particle of 2 mass m will have a definite parity: H = P² + 1m²x². (200 words)
(d)) An electron with a energy of 8.0 eV strikes a potential barrier of energy 12.0 eV. If the tunnelling probability is 4.0 percent, determine the width of the barrier. (200 words)

Key Points:

Particle in a box eigenfunctions are not eigenfunctions of the momentum operator.
Expectation value of kinetic energy for particle in a box is E_n = ħ²n²π²/(2mL²).
Probability current density J = (ħ/2im)(Ψ* ∂Ψ/∂x - Ψ ∂Ψ*/∂x).
For incident wave Ψ_inc = A e^(ikx), J_inc = (ħk/m)|A|².

Answer: This response provides a comprehensive analysis of fundamental quantum mechanics problems, drawing upon concepts typically covered in the BPHET-141 course. It addresses the properties of eigenfunctions for a particle in a box, calculates expectation values, derives probability current densities for step potentials, explores the concept of parity in quantum systems, and applies the tunneling probability formula to determine barrier width. Each sub-question is tackled with detailed explanations, s...

Q4. Answer the following questions:

(a)) The half-life of 14 C is known to be 5730 years. Calculate the decay constant (in s¯¹). Also, calculate the rate of disintegration for 1 g of 14C. (200 words)
(b)) Calculate the kinetic energy of the alpha particle emitted in the alpha decay of the Radium isotope 88 Ra 226 m(Ra) 226 Ra → Rn+2 He). 222 He. It is given that m88Ra = 226.0254 u , m(He) = 4.0026 u and m 86Rn | = 222.0176u. (200 words)
(c)) From the semi-empirical mass formula, calculate the value of the atomic number (Z) for the most stable nucleus at a given mass number A. Calculate Zo for A = 90. (400 words)
(d)) Two tritium H nuclei fuse to release 11.3 MeV energy. Calculate the total energy released in the fusion of 1 kg tritium. (200 words)

Key Points:

Radioactive decay constant λ = ln(2) / T₁/₂, where T₁/₂ is the half-life.
Activity (rate of disintegration) R = λN, with N being the number of radioactive atoms.
Q-value of a nuclear reaction is energy released from mass defect (Δm), Q = Δm × 931.5 MeV/u.
Alpha particle kinetic energy K_α = Q × [m(daughter) / (m(daughter) + m(alpha))] due to momentum conservation.

Answer: Nuclear physics deals with the structure, properties, and interactions of atomic nuclei. This includes phenomena like radioactive decay, nuclear reactions such as alpha decay and fusion, and the theoretical understanding of nuclear stability. The semi-empirical mass formula provides a crucial framework for predicting nuclear properties like binding energy and identifying stable isotopes. The following solutions apply these fundamental principles to specific problems.

BPHET-141 Solved Assignment — January 2026 / July 2026

ELEMENTS OF MODERN PHYSICS | IGNOU Bachelor of Science (General) (CBCS) (BSCG)

BPHET-141—January 2026 / July 2026

ELEMENTS OF MODERN PHYSICS

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