The four quantum numbers n, l, m_l, m_s specify an electron’s state in an atom. n determines the energy level and roughly the size of the orbital. l identifies the subshell type and the orbital’s shape (0 for s, 1 for p, 2 for d, 3 for f). m_l gives the orbital’s orientation in space within that subshell, with values from -l to +l. m_s describes the electron’s intrinsic spin direction, with possible values of +1/2 or -1/2. Together, these four numbers uniquely describe the orbital and the spin state of the electron. This set uses the standard symbols and order, corresponding to energy level, subshell shape, orbital orientation, and electron spin. Other options either replace n with an unfamiliar symbol, omit the spin quantum number, or position the spin value before the orbital orientation, which does not align with how these quantum numbers are defined.

Actual yield is the amount of product you actually obtain from a reaction run in the lab. Theoretical yield is the maximum amount that could be formed from the given reactants, calculated by stoichiometry assuming the reaction goes to completion with no losses. A predicted yield from a calculation usually refers to that theoretical amount, not what you recover in reality. Leftover reactants represent what you didn’t convert into product, not the yield itself. In real experiments, the actual yield is often lower than the theoretical yield due to incomplete reactions, side reactions, and losses during purification or transfer. To assess efficiency, you compare actual yield to theoretical yield using percent yield = (actual yield / theoretical yield) × 100%.

Valence electrons are the electrons in the outermost energy level of an atom. They sit farthest from the nucleus and are the ones most readily involved in bonding, so they largely determine an element’s chemical properties. Inner, or core, electrons stay closer to the nucleus and don’t participate in bonding to the same extent. Neutrons are not electrons at all; they reside in the nucleus and don’t affect chemical bonding. The outermost energy level, or highest principal quantum number shell, is where these valence electrons live, and that’s why this region is key to reactivity. For example, sodium has one valence electron in its outer shell, while chlorine has seven, which helps explain their tendency to form NaCl.

Isotopes differ in the number of neutrons while keeping the same number of protons. Potassium has 19 protons, so a neutral potassium atom also has 19 electrons. The two isotopes shown have mass numbers 39 and 40, which means their neutron counts are 39 − 19 = 20 and 40 − 19 = 21, respectively. Therefore, the quantity that differs is the number of neutrons. Since neutrons change, the mass number also changes, but the defining difference between isotopes is the neutron count.

Ksp is the solubility product constant for a sparingly soluble salt, representing the equilibrium condition when the solid is present and the solution is saturated. For a dissolution like MX(s) ⇌ M+(aq) + X−(aq), Ksp = [M+][X−]. More generally, for a salt with stoichiometry aA^(n+) + bB^(m−) ⇌ ... the Ksp is the product of the ion concentrations raised to their coefficients, evaluated at saturation. This product is constant at a given temperature, reflecting the balance between dissolution and precipitation. The concept here is that the dissolved ion concentrations settle to fixed values that satisfy this product, regardless of how much solid remains or is consumed, as long as the system is at equilibrium. So the statement that Ksp is the product of ion concentrations at saturation captures the essence: it’s the equilibrium constant for the dissolution process, not a simple sum of concentrations, not a rate constant for precipitation, and not a constant for gas dissolution.