Physics Chapter on Photoelectric Effect and Forces

The work function is the minimum energy required to remove an electron from the surface of a material.

A photoelectric device can operate with a given light source if the photon energy (hν) is greater than or equal to the work function (ϕ) of the material.

Ultraviolet light has higher energy photons than visible light. Sodium's lower work function allows it to be stimulated by UV light.

The dimensions of a quantity are the fundamental units it is composed of, like length, mass, and time.

The dimensions of GIM2 / E2 can be determined by analyzing the dimensions of each component:

• G (gravitational constant) has dimensions of [M-1L3T-2]
• I (impulse) has dimensions of [MLT-1]
• M (mass) has dimensions of [M]
• E (energy) has dimensions of [ML2T-2].

Work done by a force is the integral of the force along the path of motion.

In this case, the work done is the line integral of the force F from (0, 0, 0) to (2, 4, 0) along the curve y = x2.

Surface tension is a property of liquids that causes the liquid to contract and minimize its surface area.

A charged soap bubble experiences an outward pressure due to electrostatic repulsion. This pressure balances the inward pressure due to surface tension just before bursting.

The radius of the bubble just before bursting is determined by the ratio of the surface charge density and the surface tension.

Ampere's Law relates the magnetic field around a closed loop to the current enclosed by the loop.

The magnetic field inside a long straight wire is proportional to the distance from the center of the wire.

The ratio of magnetic fields at different distances from the center of the wire can be calculated using Ampere's Law.

A transformer is a device that uses electromagnetic induction to change the voltage of an alternating current (AC).

The induced voltage in the secondary coil is proportional to the number of turns in the secondary coil and the rate of change of magnetic flux in the primary coil.

The gravitational pull between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.

The gravitational pull between the sphere and the point mass depends on the mass distribution of the sphere. Note that any point mass inside the sphere is not attracted by the matter outside the Gaussian surface.

Beats are a phenomenon that occurs when two sound waves with slightly different frequencies interfere with each other. The result is a periodic variation in loudness and quietness.

Superposition of waves requires that the frequencies of the waves are similar or equal.

The electric potential due to a dipole is proportional to the dipole moment and inversely proportional to the distance from the dipole.

The internal energy of a gas is directly proportional to its temperature. The change in internal energy is determined by the change in temperature and the gas's heat capacity.

The de Broglie wavelength of a particle is inversely proportional to its momentum. The wavelength of a photon is inversely proportional to its energy.

The ratio of the de Broglie wavelength of a proton to the wavelength of a photon is proportional to E-1/2. This is because the energy of the proton is equal to the energy of the photon.

In thermodynamics, a cyclic process is one in which the system returns to its initial state after a series of changes. This means that net work done and net heat transfer are both zero.

A perfectly elastic collision is a collision where kinetic energy is conserved. The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

The maximum energy stored in the spring is equal to the initial kinetic energy of block A, assuming a perfectly elastic collision with block B.

Kirchhoff's Laws are used to analyze circuits. Kirchhoff's Current Law states that the algebraic sum of currents entering a junction in a circuit is equal to the algebraic sum of currents leaving the junction.

Diffraction is the bending of waves as they pass through an opening or around an obstacle.

The width of diffraction bands is inversely proportional to the wavelength of light. Blue light has a shorter wavelength than red light, so the diffraction bands will be narrower and closer together.

A screw gauge is a precision instrument used to measure the diameter of small objects, such as wires.

The diameter of the wire can be calculated by adding the main scale reading and the circular scale reading multiplied by the least count.

The escape velocity is the minimum velocity an object needs to escape the gravitational pull of a planet.

The escape velocity is directly proportional to the square root of the product of the planet's density and radius. Higher density and larger radius mean a higher escape velocity.

A Zener diode is a type of diode designed to operate in the reverse breakdown region. At the break-down voltage called the Zener voltage, current flows through the diode, allowing for voltage regulation.

The current through the Zener diode is determined by the difference between the input voltage and the Zener voltage, divided by the Zener diode's resistance.

Mutual inductance is a property of two coils that describes the ability of one coil to induce a voltage in the other coil.

Mutual inductance is proportional to the number of turns in each coil, the area of cross-section, and the permeability of the core material.

The total distance traveled is the sum of the distances traveled during each segment of the motion. Distance traveled during retardation is the sum of the distances traveled when the particle is decelerating.

The midpoint of a system of connected objects moves a distance that is proportional to the relative extensions of the two parts of the system.

The angle rotated by the rod BC can be calculated using conservation of angular momentum. When the rod breaks, the angular momentum is conserved.

The solubility product (Ksp) is the equilibrium constant for the dissolution of a sparingly soluble ionic compound. These values express the extent to which an ionic compound dissolves in water.

The concentration of Ag+ ions in a solution is determined by the solubility product of the Ag+ salt and the presence of any complexing ligands.

Ionization enthalpy is the energy required to remove an electron from a gaseous atom or ion. The second ionization enthalpy involves removing an electron from a +1 ion.

The compound shown is pyridine, a heterocyclic aromatic compound. The nitrogen atom exhibits sp2 hybridization.

The stability and properties of halide compounds are influenced by various factors, including the size of the metal, the size of the halogen, and the electronegativity differences. Generally, the stability of halides increases down a group. However, the ability to form halides also depends on the nature of the metal.

In general, oxides react with water to form acids, while basic oxides react with water to form bases. Amphoteric oxides can act as either acids or bases depending on the reaction conditions.

Bond order is a measure of the number of chemical bonds between two atoms. A higher bond order indicates a stronger bond.

When an atom de-excites from a higher energy level to a lower energy level, it emits a photon of light. The energy of the photon corresponds to the energy difference between the two levels.

The Paschen series corresponds to transitions where the final energy level is n = 3. Similarly, the Brackett series corresponds to transitions where the final energy level is n = 4.

Lewis acids are electron-pair acceptors, while Lewis bases are electron-pair donors. Boron halides are typically Lewis acids due to their incomplete octets.

The enthalpy of hydrogenation is the enthalpy change associated with the addition of hydrogen gas to an unsaturated molecule. It can be used to calculate resonance energy when comparing theoretical enthalpy of hydrogenation with the experimental value.

Lanthanides are a group of fourteen elements with atomic numbers 57 through 70. They all belong to the f-block of the periodic table.

The activation energy of a reaction is the minimum amount of energy required for the reaction to occur. The overall activation energy of a complex reaction can be calculated from the activation energies of individual steps in the reaction mechanism.

Aromatic compounds are cyclic, planar molecules with a system of delocalized π electrons, following Hückel's rule (4n+2) π electrons. These compounds exhibit extraordinary stability compared to similar non-aromatic molecules.

The sequence of reactions involves a series of transformations. The use of NaNH2 suggests a deprotonation step, and the presence of HgSO4 indicates a hydration step.

In the Sn1 reaction, the rate determining step is the formation of the carbocation intermediate. This intermediate is stabilized by electron donating groups attached to the carbon.

Oxidizing agents gain electrons and reducing agents lose electrons. A substance can be both an oxidizing and a reducing agent if it contains an element with a variable oxidation state.

Coordination number is the number of atoms or molecules directly bonded to a central metal atom in a complex. Typically, a metal with a coordination number of 4 can have either a square planar or tetrahedral geometry.

The IUPAC naming of coordination compounds follows specific rules. The name starts with the cation, followed by the anion.

The reaction sequence involves the use of reagents to selectively transform the starting material. The reactions could involve oxidation, reduction, or substitution.

The percentage by mass of Fe in the original sample can be calculated by subtracting the mass of the residue from the original mass of the mixture. The difference in mass is due to the loss of oxygen during the decomposition of Fe2O3.

An equilibrium constant is a measure of the relative amounts of reactants and products present at equilibrium. It can be determined by dividing the product of the concentrations of the products raised to their stoichiometric coefficients by the product of the concentrations of the reactants raised to their stoichiometric coefficients.

Freezing point depression is a colligative property that describes the lowering of the freezing point of a solvent when a non-volatile solute is added. The molar mass of the solute can be determined using the freezing point depression constant, the change in freezing point, and the molality of the solution.

The Nernst equation relates the cell potential of an electrochemical cell to the standard cell potential, the temperature, and the concentrations of the reactants and products. It can be used to calculate the cell potential at non-standard conditions.

The carbylamine test is a chemical test used to identify primary amines. In this test, a primary amine is heated with chloroform in the presence of an alcoholic potassium hydroxide solution, producing a foul-smelling isocyanide (carbylamine).

A function is differentiable at a point if the derivative exists at that point. The derivative of a function measures the rate of change of the function with respect to its input variable.

A system of linear equations has a unique solution if and only if the determinant of the coefficient matrix is non-zero. The determinant of a matrix is a single number that provides information about the properties of the matrix.

Leibniz's rule is a rule for differentiating integrals with respect to a parameter. It is used to differentiate an integral whose limits of integration depend on the parameter of differentiation.

The magnitude of a complex number is determined by the Pythagorean theorem. The magnitude of a complex number is always a non-negative real number.

The roots of a polynomial equation are the values of the variable that make the equation true. If the roots of a polynomial equation are related, there may be relationships between the coefficients of the polynomial.

Definite integrals can be used to calculate the area of a region bounded by curves. To solve this problem, you can graph the given function and use the knowledge of trigonometric functions to find the area.

A function is continuous at a point if the limit of the function as x approaches the point exists and is equal to the value of the function at that point. To check if a function is differentiable, you can check if it's also continuous at the given point.

Combinations are a mathematical way of selecting items from a set without regard to order. The number of combinations of n items taken r at a time is denoted by nCr and is calculated using the formula nCr = n! / (r! * (n-r)!).

A hyperbola is a conic section with two branches that are symmetric about its center. Its eccentricity, a measure of how 'stretched' it is, determines its shape.

An ellipse is a conic section that looks like a stretched circle. Its eccentricity, a measure of how 'oval-shaped' it is, determines its shape.

The area of a circle is given by the formula A = πr2, where r is the radius of the circle. The radius of a circle is the distance from the center of the circle to any point on the circle.

The standard deviation measures the spread or variability of data points in a dataset relative to the mean. The standard deviation is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean.