General Chemistry I: Atomic Structure, Radioactivity, and Quantum Concepts – Exam Study Guide

Atomic Structure and Fundamental Constants

Key Physical Constants and Equations

This section provides essential constants and equations frequently used in general chemistry, especially for calculations involving atoms, photons, and subatomic particles.

• Avogadro's Number (N0): $6.022 \times 10^{23}$

• Speed of Light (c): $3.00 \times 10^8$ m/s

• Planck's Constant (h): $6.626 \times 10^{-34}$ J·s

• Rydberg Constant (R): $1.0974 \times 10^7$ m-1

• Energy of a Photon: $E = h\nu$

• Photon Energy and Wavelength: $E = \frac{hc}{\lambda}$

• Energy of an Electron (Kinetic): $E = \Phi + \frac{1}{2}mv^2$

• Hydrogen Atom Energy Levels: $E_n = -\frac{Rhc}{n^2}$

• Wavelength and Momentum: $\lambda = \frac{h}{mv}$

• Mass of Electron: $9.11 \times 10^{-31}$ kg

• Mass of Proton: $1.67 \times 10^{-27}$ kg

• 1 nm = $1 \times 10^{-9}$ m

Example: To find the energy of a photon with wavelength 500 nm, use $E = \frac{hc}{\lambda}$.

Radioactivity and Nuclear Chemistry

Alpha Decay and Nuclear Symbols

Radioactive decay involves the transformation of unstable nuclei into more stable forms, often by emitting particles such as alpha particles.

• Alpha (α) Decay: The emission of an alpha particle, which is a helium nucleus consisting of 2 protons and 2 neutrons.

• Nuclear Symbol for Alpha Particle: $^4_2\text{He}^{2+}$ or $\alpha$

• Example: Americium-243 ($^{243}_{95}\text{Am}$) undergoing alpha decay produces $^{239}_{93}\text{Np}$ and an alpha particle.

Application: If an isotope of americium with 146 neutrons decays by alpha emission, subtract 2 protons and 2 neutrons from the original nucleus to determine the product.

Millikan Oil Drop Experiment and Charge Quantization

Experimental Setup and Modifications

The Millikan oil drop experiment was designed to measure the elementary charge of the electron by observing the motion of oil droplets in an electric field.

• Original Setup: Oil droplets are suspended between two charged plates; their motion is observed to determine the charge.

• Modification for Positrons: Replace the electron source with a positron source. The direction of the electric field must be reversed to account for the positive charge of positrons.

• Reason for Modification: Positrons are positively charged, so the field must be oriented to counteract gravity for positive charges, not negative.

Charge Quantization Table

Millikan's experiment demonstrated that charge is quantized in integer multiples of the elementary charge ($e$). For positrons, the measured charges should also be integer multiples of $+e$.

Total droplet charge	Number of positrons
+4.8066 × 10-19 C	3
+9.6125 × 10-19 C	6
+11.2154 × 10-19 C	7
+17.6224 × 10-19 C	11
+20.8286 × 10-19 C	13

Additional info: The number of positrons is calculated by dividing the total charge by the elementary charge ($e = 1.6022 \times 10^{-19}$ C).

Isotopic Abundance and Atomic Mass

Calculating Percent Abundance

Atomic mass is the weighted average of the masses of an element's isotopes, based on their natural abundances.

• Formula: $\text{Average atomic mass} = (\text{fraction}_1 \times \text{mass}_1) + (\text{fraction}_2 \times \text{mass}_2)$

• Example: If an element has isotopes of 36.8462 amu and 39.1283 amu, and the average atomic mass is 37.1234 amu, set up equations to solve for the percent abundance of each isotope.

Photoelectric Effect and Ionization Energy

Threshold Energy and Wavelength

The photoelectric effect describes the emission of electrons from a metal surface when light of sufficient energy strikes it. The minimum energy required to remove an electron is called the work function (Φ).

• Work Function (Φ): The minimum energy needed to eject an electron from a metal surface.

• Photoelectric Equation: $E = \Phi + \frac{1}{2}mv^2$

• Threshold Wavelength: $\lambda = \frac{hc}{\Phi}$

• Application: To find the longest wavelength capable of ejecting an electron, use the threshold energy in the equation above.

Example: For platinum, if the work function is known, calculate the threshold wavelength in nm.

Quantum Numbers and Electron Configuration

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them.

• Principal Quantum Number (n): Indicates the energy level (shell).

• Angular Momentum Quantum Number (l): Indicates the subshell (0 = s, 1 = p, 2 = d, 3 = f).

• Magnetic Quantum Number (ml): Specifies the orbital within the subshell.

• Spin Quantum Number (ms): Specifies the electron's spin (+1/2 or -1/2).

Example: The quantum numbers for the 1s electron in hydrogen are n = 1, l = 0, ml = 0, ms = +1/2.

Periodic Trends: Electron Affinity, Atomic Size, and Ionization Energy

Comparing Atomic and Ionic Properties

Periodic trends help predict and compare the properties of elements and ions.

• Electron Affinity: The energy change when an electron is added to a neutral atom. More negative values indicate a greater tendency to gain electrons.

• Atomic/Ionic Size: Cations are smaller than their parent atoms; anions are larger. Size increases down a group and decreases across a period.

• Ionization Energy: The energy required to remove an electron from a gaseous atom or ion. Increases across a period and decreases down a group.

Example: Among Mg2+, Si0, S2-, P, and Cl2-, S2- is the largest due to increased electron-electron repulsion.

Summary Table: Periodic Trends

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Becomes more negative	Becomes less negative

Additional Info

• Some questions reference pop culture (e.g., Star Wars) for engagement but are not chemistry content.

• All calculations should include appropriate units (e.g., g, Hz, m, J, etc.).