PHE-11 Solved Assignment January 2026 | Modern Physics | IGNOU BSC

Q1. Attempt all questions. Symbols have their usual meanings. The marks for each question are indicated against it.

a)) A muon decays spontaneously into an electron and two neutrinos. If the number of muons at t = 0 is No and the number at time t is N where N is given by the expression N = Noe¯t/t . The mean lifetime of the muon is t = 2.20µs. If the muons are travelling with a speed of 0.95c, calculate the observed lifetime of the muons and the number of muons which remain after travelling a distance of 3.0 km. (200 words)
b)) Two rockets of rest length Lo are approaching the earth from opposite directions with velocities of ±c/3. How long would one of them appear to the other? (200 words)
c)) How fast and in what direction must a galaxy S be moving, if an absorbtion line observed at a wavelength of 550 nm for a stationary galaxy is shifted to 430 nm for S. (200 words)
d)) Electrons in a television set are accelerated through a potential difference of 40 kV. Assuming that the electrons start from rest, calculate their velocity using the relativistic equation for the kinetic energy. (200 words)
e)) A particle of mass M, initially at rest, decays into two particles with rest masses m₁ and m2 respectively. Show that the total energy of the mass m₁ is: E₁ = c² [M² + m² - m²] / 2M (200 words)

Key Points:

Time dilation: Moving clocks run slower, observed lifetime τ = γτ₀.
Length contraction: Moving objects appear shorter, observed length L = L₀/γ.
Relativistic Doppler Effect: Wavelength shift indicates relative speed and direction.
Relativistic Kinetic Energy: K.E. = (γ-1)mc² for particles near light speed.

Answer: This question delves into several fundamental concepts of Modern Physics, primarily Special Relativity, applying its principles to real-world phenomena like particle decay, interstellar travel, and astronomical observations. It covers time dilation, length contraction, the relativistic Doppler effect, relativistic kinetic energy, and the conservation laws in particle decay. Understanding the Lorentz factor (γ) and the interrelation between energy, momentum, and mass is crucial for solving these ...

Q2. Answer the following questions:

a)) Calculate the de Broglie wavelength of an electron in the first Bohr orbit of the hydrogen atom. (200 words)
b)) A photon and an electron each have an energy of 6.0×10³ eV. What are their wavelengths? Which of these would you use to probe atomic structures? (200 words)
c)) Determine the normalization constant N for the following wavefunction: ψ(r, t) = Ne^(iEt/ħ) * r^(mZq²/ħ² * 2), where (r, t) is defined over 0 ≤ r ≤ ∞, E is the energy, Z is a constant, q is the charge of the electron, and m is the mass of the particle. (200 words)
d)) Estimate the minimum kinetic energy a proton confined to a nucleus of diameter 10^-15 m may have. (200 words)
e)) Show that i) x, e^(iap/ħ) = ae^(iap/ħ) ii) [Ly, Lz] = iħ Lx (200 words)

Key Points:

De Broglie wavelength for electron in first Bohr orbit is 2πa₀.
Photon wavelength calculated via E=hc/λ; electron wavelength via λ=h/√(2mE).
Physical wavefunctions must be normalizable; integral ∫|ψ|²dV must be finite.
Heisenberg Uncertainty Principle (ΔxΔp ≈ ħ) estimates minimum confined particle energy.

Answer: This answer addresses fundamental concepts in Modern Physics, covering de Broglie wavelength calculations, wavefunction normalization, and quantum mechanical operators. Sub-questions delve into specific applications like estimating particle energies in confined spaces and deriving commutation relations for angular momentum operators. All calculations are shown step-by-step, and theoretical explanations are provided to ensure a comprehensive understanding of the underlying principles from the PH...

Q3. Answer the following questions:

a)) The normalised eigenfunctions of a simple harmonic oscillator are given by ψn(x) = (a/(sqrt(pi) * 2^n * n!))^(1/2) * Hn(ax) * exp(-a²x²/2), n = 0, 1, 2,... Calculate < x > and <px > for the ground state harmonic oscillator eigenfunction. (400 words)
b)) X-rays from a cobalt (Z = 27) tube have a strong K line of wavelength 1.785 Å and a weak line due to chromium impurity (Z = 24). Using Moseley's law, calculate the wavelength of the weak line. (200 words)
c)) (i) Determine the average kinetic energy of the hydrogen atom in its ground state. (ii) Using the uncertainty relation, show that the dimension of the most stable ground state of the hydrogen atom is of the order of the first Bohr radius. (400 words)

Key Points:

Ground state harmonic oscillator expectation values for position (<x>) and momentum (<px>) are zero due to wave function symmetry.
Moseley's Law: √ν = a(Z - b) relates characteristic X-ray frequency to atomic number.
For K-series X-rays, the screening constant 'b' is approximately 1.
Hydrogen atom's average kinetic energy in ground state is +13.6 eV, derived from Virial Theorem (E = -<T>).

Answer: This response addresses key concepts in Modern Physics, covering quantum mechanics of the simple harmonic oscillator, atomic structure as described by Moseley's Law, and the fundamental properties of the hydrogen atom derived from quantum principles. It includes calculations for expectation values, X-ray wavelengths, and demonstrates how quantum uncertainty leads to the characteristic atomic size. Sub-question (a) delves into the quantum mechanical properties of the simple harmonic oscillator, ...

Q4. Answer the following questions:

a)) A radioactive sample emits n ẞ-particles in 2s. In next 2s it emits 0.75 n ẞ-particles. Calculate the mean life of the sample? (300 words)
b)) In a nuclear reactor 235U undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 years, find the total mass of uranium required. (250 words)
c)) Describe the principle and working of a cyclotron. Derive an expression of the maximum kinetic energy of the particle when it reaches the outermost radius of the cyclotron. (300 words)
d)) Write the charge, baryon number and spin of a photon and a proton. (150 words)

Key Points:

Mean life (τ) is the reciprocal of the decay constant (λ) from activity ratios.
Nuclear reactor U-235 mass is calculated from total energy, efficiency, and energy per fission.
Cyclotron accelerates charged particles using perpendicular magnetic and alternating electric fields.
Maximum kinetic energy in a cyclotron: KE_max = q²B²R² / (2m).

Answer: This answer addresses four distinct problems from the PHE-11 Modern Physics course, covering radioactive decay, nuclear reactor calculations, cyclotron physics, and fundamental particle properties. Each sub-question is answered comprehensively, adhering to the specified word limits and incorporating detailed explanations and step-by-step calculations where applicable. The principles and applications of modern physics concepts are highlighted throughout, consistent with an IGNOU curriculum. For...

PHE-11 Solved Assignment — January 2026 / July 2026

Modern Physics | IGNOU foKku esa Lukrad mikf/k dk;ZØe (ch-,l-lh-) (BSC)

PHE-11—January 2026 / July 2026

Modern Physics

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PHE-11 Assignment Questions — January 2026

Q1. Attempt all questions. Symbols have their usual meanings. The marks for each question are indicated against it.

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