Physics

The effective mass of a photon can be estimated using its energy and the relation E = mc². For a photon of wavelength 900 nm, the equivalent mass is approximately 2.46 x 10⁻³⁶ kg, matching option C.

The linear momentum p of a photon is given by p = h/λ, where h is Planck's constant (6.626 x 10^-34 Js) and λ is the wavelength. For λ = 0.1 Å = 1 x 10^-11 m, p = 6.626 x 10^-34 / 1 x 10^-11 = 6.626 x 10^-23 kg·m/s (or N·s). None of the provided options match this value or its order of magnitude, so the data is insufficient or options are incorrect.

Simple harmonic motion is a type of vibratory motion where an object oscillates back and forth about an equilibrium position in a periodic manner.

A photon has zero rest mass but carries momentum given by p = hv/c, where h is Planck's constant, v is frequency, and c is the speed of light. Therefore, the correct expression for photon momentum is hv/c.

When a convex lens (with positive focal length f1) and a concave lens (with negative focal length f2) are placed in contact, the combined focal length F is given by the lens combination formula: 1/F = 1/f1 + 1/f2. Rearranging, F = (f1 * f2) / (f1 + f2). Since f2 is negative, the denominator becomes (f1 - |f2|), which matches option D's formula. This formula correctly accounts for the sign conventions of convex and concave lenses and gives the effective focal length of the combination.

According to the Heisenberg uncertainty principle, confining an electron to a very small region (on the order of 10^-14 m) implies a very large uncertainty in its momentum. If one uses the classical non-relativistic relation p = mv, this large momentum uncertainty would correspond to a speed greater than the speed of light, which is not physically possible. This indicates that classical physics breaks down at such scales and relativistic quantum mechanics must be used. The relativistic relation between momentum and velocity ensures the electron's speed remains below the speed of light, but the kinetic energy required to confine the electron so tightly becomes extremely large, signaling the need for quantum field theory treatment. Therefore, the statement that the electron's speed should be greater than the speed of light if confined to such a small radius is conceptually correct in the classical sense, highlighting the breakdown of classical assumptions. Hence, option B is correct.

According to special relativity, an object moving at relativistic speeds relative to an observer appears length contracted along the direction of motion. Therefore, the observer measures the meter stick's length as less than one meter.

The restoring force causing the simple pendulum to oscillate is the component of the gravitational force acting along the arc of the pendulum's swing, which is mg sinθ. This force pulls the pendulum back toward its equilibrium position, causing vibratory motion.

The magnifying power of a simple microscope is inversely proportional to the focal length of its lens; thus, as the focal length decreases, the magnifying power increases.

Michelson used an interferometer to measure the speed of light with high precision. The interferometer allowed him to detect very small changes in the light path length, enabling accurate calculation of light speed.