In the Geiger-Marsden experiment, approximately what fraction of the incident α-particles scattered by more than 90°?

An α-particle with initial kinetic energy K undergoes a head-on collision with a gold nucleus (charge Ze). The distance of closest approach (d) is proportional to:

For an electron revolving in a dynamically stable orbit of radius r in a hydrogen atom, the relation between the orbit radius and the electron velocity (v) is given by:

According to classical electromagnetic theory, an electron revolving around a proton in a hydrogen atom (radius 5.3 × 10⁻¹¹ m, velocity 2.2 × 10⁶ m/s) should emit radiation with an initial frequency (ν) of approximately:

The atomic mass unit (u) is defined such that 1 u is equal to approximately:

Nuclides such as ¹⁹⁸₈₀Hg and ¹⁹⁷₇₉Au are categorized together because they share the same:

The constant R₀ in the nuclear radius formula R = R₀A¹/³ is approximately 1.2 × 10⁻¹⁵ m. This unit is called:

The total mass of a stable nucleus (M) is less than the sum of the masses of its protons and neutrons (Σm). The difference ΔM is called the mass defect, and the binding energy (Eb) is given by:

The binding energy per nucleon (Ebn) curve shows a maximum value of about 8.75 MeV for nuclei near which mass number (A)?

A material where the valence band is completely filled and the conduction band is completely empty, separated by a large band gap (Eg > 3 eV), is a/an:

If a pure Si crystal (atomic concentration = 5 × 10²⁸ m⁻³) is doped with 1 ppm pentavalent As, and intrinsic carrier concentration ni = 1.5 × 10¹⁶ m⁻³, the resultant hole concentration (nh) will be:

When a tetravalent semiconductor is doped with a trivalent impurity acceptor, the resulting energy level (EA) exists:

A silicon diode typically exhibits a threshold voltage (cut-in voltage) of approximately:

The dynamic resistance (rd) of a p-n junction diode is the ratio of a small voltage change (ΔV) to a small current change (ΔI). In reverse bias saturation, rd is typically:

A point charge Q is placed at the origin. What is the ratio of the magnitude of the electric field (E) to the magnitude of the electric potential (V) at a distance r from the charge?

A small planar element of area ΔS is placed in a uniform electric field E. If the electric flux Δφ = E ΔS cosθ, what condition must be met for θ = 0°?

The work done by an external force W₍RP₎ in moving a charge q from point R to point P increases its potential energy. If W₍RP₎ is positive, this implies that the external force performed work against the:

The electric potential V due to an electric dipole at large distances (r >> a) falls off proportional to:

The average drift speed of electrons in copper is about 1.1 × 10⁻³ m/s. By what factor is this smaller than the propagation speed of the electric field (≈ 3.0 × 10⁸ m/s)?

In a Wheatstone bridge of resistors R₁ (AB), R₂ (BC), R₃ (CD), and R₄ (DA), with galvanometer BD, the bridge is balanced when:

The magnetic field B along the axis of a circular loop (radius R, current I) at distance x from center is proportional to:

A charge q moving with velocity v in magnetic field B experiences zero magnetic force when:

Ampere’s circuital law simplifies calculations when B is tangential and constant along the loop. Which condition is NOT sufficient?

A diamagnetic substance exhibits weak repulsion in a magnetic field. Its relative permeability μ_r lies in the range:

Which property follows directly from the non-existence of magnetic monopoles?

Which ratio in magnetism is analogous to dielectric constant K in electrostatics?

Self-inductance L is a measure of a coil’s opposition to current change. It is analogous to which mechanical property?

In an AC generator, induced emf ε is maximum when the area vector A of the coil makes which angle θ with magnetic field B?

A straight conductor of length l moves with velocity v perpendicular to magnetic field B. The work done by Lorentz force on charge q is:

A series LCR circuit has an inductor L = 25.48 mH and a capacitor C = 796 μF. If the circuit is connected to an ac source, what is the resonant frequency ν₀ in Hz?

The standard household line voltage of 220 V is an rms value. What is the peak voltage (vₘ) of this supply?

A 15.0 μF capacitor is connected to a 220 V, 50 Hz source. Calculate the capacitive reactance (Xc) (Use π ≈ 3.14).

Which of the following expressions represents the mathematical form of the generalised Ampere-Maxwell law?

The speed of an electromagnetic wave (c) in vacuum is determined by which combination of fundamental constants?

If the peak electric field amplitude (E₀) in an electromagnetic wave is 120 N/C, what is the peak magnetic field amplitude (B₀)? (c ≈ 3 × 10⁸ m/s).

A glass lens (refractive index n = 1.47) is submerged in a liquid and disappears. What condition is met by the refractive index of the liquid (n_liquid) and the resulting focal length (f) of the lens in the liquid?

Which two conditions must be met simultaneously for total internal reflection (TIR) to occur at an interface between two media?

An object is placed at u = -10 cm in front of a concave mirror with focal length f = -7.5 cm. What is the image distance v?

Two coherent sources produce waves such that the phase difference at a point P is φ. If I₀ is the intensity due to each individual source, what is the resultant intensity I at P?

For two independent light sources illuminating a wall, no stable interference fringes are observed. This happens because the sources are typically incoherent. Incoherent sources are characterized by:

For destructive interference between two coherent sources vibrating in phase, the path difference (S₁P − S₂P) must be equal to: where n = 0, 1, 2, ... and λ is wavelength.

Calculate the de Broglie wavelength (λ) associated with a macroscopic ball of mass 150 g travelling at 30.0 m/s. (h = 6.63 × 10⁻³⁴ J·s)

What is the threshold frequency (ν₀) for a photosensitive metal defined as, in relation to the work function (φ₀)?

In the experimental study of the photoelectric effect, the stopping potential (V₀) for a given photosensitive material depends linearly on: