Atoms, Molecules, and Nuclear Chemistry
Atoms, Molecules, and Nuclear Chemistry MCQ Questions
7.
The maximum number of electrons that can be accommodated in the nth shell of an atom is given by the formula:
Approach
The question asks for the maximum number of electrons that can be accommodated in a given electron shell, denoted by 'n'. This concept is fundamental to understanding atomic structure and electron configuration, often explained by Bohr's model and quantum mechanics principles.
Step-by-step
- Understanding Electron Shells: In an atom, electrons occupy specific energy levels or shells around the nucleus. These shells are numbered starting from the innermost shell as \(n=1\), \(n=2\), \(n=3\), and so on.
- Bohr-Bury Rules: According to the Bohr-Bury rules for electron distribution, the maximum number of electrons that can be accommodated in a particular shell is determined by a specific formula.
- Deriving the Formula: Each shell 'n' can contain 'n' subshells. Each subshell 'l' (where \(l = 0, 1, ..., n-1\)) has \(2l+1\) orbitals. Each orbital can hold a maximum of 2 electrons (Pauli Exclusion Principle). Summing these up for a given shell 'n':
- For \(n=1\) (K-shell), \(l=0\) (s-subshell). Number of orbitals \(2(0)+1 = 1\). Max electrons = \(1 \times 2 = 2\).
- For \(n=2\) (L-shell), \(l=0\) (s-subshell) and \(l=1\) (p-subshell). Number of orbitals for \(l=0\) is 1. Number of orbitals for \(l=1\) is \(2(1)+1 = 3\). Total orbitals = \(1+3 = 4\). Max electrons = \(4 \times 2 = 8\).
- For \(n=3\) (M-shell), \(l=0\) (s-subshell), \(l=1\) (p-subshell), \(l=2\) (d-subshell). Number of orbitals for \(l=0\) is 1. Number of orbitals for \(l=1\) is 3. Number of orbitals for \(l=2\) is \(2(2)+1 = 5\). Total orbitals = \(1+3+5 = 9\). Max electrons = \(9 \times 2 = 18\).
- Identifying the Pattern: From the examples above, we can see a pattern: the total number of orbitals in a shell 'n' is \(n^2\). Since each orbital can hold a maximum of 2 electrons, the maximum number of electrons in the nth shell is \(2 \times n^2\).
- Applying the Formula: The formula that represents this relationship is \(2n^2\).
Correct Option: C) \(2n^2\) is the correct formula for the maximum number of electrons that can be accommodated in the nth shell of an atom.
Incorrect Options
- A) \(2n\) — This formula does not correctly represent the maximum electron capacity of shells beyond the first shell. For \(n=2\), it would give \(2 \times 2 = 4\) electrons, but the L-shell can hold 8 electrons.
- B) \(n^2\) — This formula represents the total number of orbitals in the nth shell, not the maximum number of electrons. Since each orbital can hold 2 electrons, the
8.
The electronic configuration of sodium (atomic number 11) is:
Approach
The electronic configuration of an atom describes the distribution of electrons in its atomic orbitals. For the first 20 elements, electrons fill shells in a predictable pattern: the first shell can hold up to 2 electrons, the second up to 8, and the third up to 18 (though for the first few elements in the third period, it fills up to 8 before the next shell starts filling).
Step-by-step
- Identify the atomic number: The atomic number of sodium is 11. This means a neutral sodium atom has 11 protons and 11 electrons.
- Fill the first shell (K-shell): The first electron shell can hold a maximum of 2 electrons. So, 2 electrons go into the first shell. Remaining electrons: \(11 - 2 = 9\).
- Fill the second shell (L-shell): The second electron shell can hold a maximum of 8 electrons. So, 8 electrons go into the second shell. Remaining electrons: \(9 - 8 = 1\).
- Fill the third shell (M-shell): The remaining 1 electron goes into the third shell.
- Combine the numbers: The electronic configuration is 2, 8, 1.
Correct Option:
C) 2, 8, 1 — This correctly represents the distribution of 11 electrons in the K, L, and M shells, respectively.
Incorrect Options
- A) 2, 8, 2 — This configuration has a total of \(2 + 8 + 2 = 12\) electrons, which is incorrect for sodium.
- B) 8, 2, 1 — This configuration places 8 electrons in the first shell, which can only hold a maximum of 2 electrons. It also totals \(8 + 2 + 1 = 11\) electrons but violates the shell capacity rules.
- D) 2, 9 — This configuration places 9 electrons in the second shell, which can only hold a maximum of 8 electrons. It also totals \(2 + 9 = 11\) electrons but violates the shell capacity rules.
9.
The atomic number of an element represents the number of:
A.
Protons present in its nucleus
B.
Electrons in its outermost shell only
C.
Neutrons present in its nucleus
D.
Total nucleons in its nucleus
ANSWER :
A. Protons present in its nucleus
Approach
The question asks about the definition of an element's atomic number. Understanding the fundamental components of an atom (protons, neutrons, and electrons) and their roles in defining an element is key to answering this question.
Step-by-step
- An atom consists of a nucleus (containing protons and neutrons) and electrons orbiting the nucleus.
- The identity of an element is determined by the number of protons in its nucleus. This number is unique for each element.
- The atomic number, symbolized by \(Z\), is defined as the number of protons in the nucleus of an atom.
- For a neutral atom, the number of electrons is equal to the number of protons. However, electrons can be gained or lost, forming ions, without changing the element's identity.
- Neutrons contribute to the mass of an atom but do not determine its atomic number or chemical identity. Atoms of the same element can have different numbers of neutrons (these are called isotopes).
Correct Option:
A) Protons present in its nucleus. The atomic number (\(Z\)) is precisely defined as the number of protons in the nucleus of an atom. This number uniquely identifies an element.
Incorrect Options
- B) Electrons in its outermost shell only. The number of electrons, especially in the outermost shell, determines an atom's chemical properties and reactivity, but not its fundamental identity or atomic number. Also, the total number of electrons can change when an atom forms an ion, while the atomic number remains constant.
- C) Neutrons present in its nucleus. The number of neutrons in the nucleus determines the isotope of an element, not the element's atomic number or identity. Different isotopes of the same element have the same atomic number but different numbers of neutrons.
- D) Total nucleons in its nucleus. Total nucleons refers to the sum of protons and neutrons in the nucleus, which is known as the mass number (\(A\)). The mass number is not the atomic number.
10.
The mass number of an atom is equal to the:
A.
Number of neutrons alone
B.
Sum of the number of electrons and neutrons
C.
Sum of the number of protons and neutrons
D.
Sum of the number of protons and electrons
ANSWER :
C. Sum of the number of protons and neutrons
Approach
The question asks for the definition of the mass number of an atom. To answer this, recall the basic structure of an atom and the components that contribute significantly to its mass.
Step-by-step
- An atom consists of a nucleus (containing protons and neutrons) and electrons orbiting the nucleus.
- Protons and neutrons are collectively known as nucleons.
- The mass of an electron is extremely small compared to that of a proton or a neutron. For practical purposes in calculating atomic mass, the mass of electrons is often considered negligible.
- The mass number (also known as atomic mass number) of an atom is defined as the total number of protons and neutrons in its nucleus. It represents the total number of nucleons.
- Mathematically, the mass number \(A\) is given by:\[ A = \text{Number of protons} + \text{Number of neutrons} \]
Correct Option:
C) Sum of the number of protons and neutrons. This is the correct definition of the mass number, as it accounts for all the significant mass-contributing particles in the atom's nucleus.
Incorrect Options
- A) Number of neutrons alone. The number of neutrons alone is not the mass number; it is only one component. The mass number also includes protons.
- B) Sum of the number of electrons and neutrons. Electrons contribute negligible mass to the atom, and protons (not electrons) are the other major component of the nucleus along with neutrons.
- D) Sum of the number of protons and electrons. While protons are crucial, electrons have negligible mass and are not part of the nucleus. The mass number is determined by the particles in the nucleus (protons and neutrons).
11.
Which of the following subatomic particles carries no electric charge?
Approach
The question asks to identify the subatomic particle that carries no electric charge. To answer this, we need to recall the basic properties (mass and charge) of common subatomic particles: electron, proton, positron, and neutron.
Step-by-step
- Recall properties of an Electron: An electron is a negatively charged subatomic particle. Its charge is \( -1.602 \times 10^{-19} \text{ C} \), often denoted as \(-1e\).
- Recall properties of a Proton: A proton is a positively charged subatomic particle found in the nucleus of an atom. Its charge is \( +1.602 \times 10^{-19} \text{ C} \), often denoted as \(+1e\).
- Recall properties of a Positron: A positron is the antiparticle of the electron. It has the same mass as an electron but carries a positive electric charge of \( +1.602 \times 10^{-19} \text{ C} \), or \(+1e\).
- Recall properties of a Neutron: A neutron is a subatomic particle found in the nucleus of an atom. It has a mass slightly greater than that of a proton but carries no net electric charge. Its charge is \(0\).
- Compare charges: Based on the properties, the neutron is the only particle among the given options that carries no electric charge.
Correct Option: D) Neutron — A neutron is an uncharged subatomic particle found in the nucleus of an atom.
Incorrect Options
- A) Electron — An electron carries a negative electric charge (\(-1e\)).
- B) Proton — A proton carries a positive electric charge (\(+1e\)).
- C) Positron — A positron carries a positive electric charge (\(+1e\)), being the antiparticle of an electron.
12.
The principle which states that no two electrons in an atom can have an identical set of all four quantum numbers is called:
A.
Heisenberg's uncertainty principle
C.
Hund's rule of maximum multiplicity
D.
Pauli's exclusion principle
ANSWER :
D. Pauli's exclusion principle
Approach
The question asks to identify the principle that states no two electrons in an atom can have the same set of all four quantum numbers. We need to recall the definitions of the given principles and rules in atomic structure.
Step-by-step
- Understanding Quantum Numbers: Each electron in an atom is described by a unique set of four quantum numbers: the principal quantum number (\(n\)), azimuthal or angular momentum quantum number (\(l\)), magnetic quantum number (\(m_l\)), and spin quantum number (\(m_s\)).
- Analyzing the statement: The statement explicitly says "no two electrons in an atom can have an identical set of all four quantum numbers." This means that if two electrons are in the same orbital (which implies identical \(n\), \(l\), and \(m_l\) values), they must differ in their spin quantum number (\(m_s\)). One will have \(m_s = +1/2\) and the other \(m_s = -1/2\).
- Relating to Pauli's Exclusion Principle: Pauli's Exclusion Principle directly states that no two electrons in an atom can have the same set of all four quantum numbers. This principle is fundamental to understanding electron configuration and the periodic table.
Correct Option:
D) Pauli's exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers (\(n\), \(l\), \(m_l\), and \(m_s\)). This means that an atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins.
Incorrect Options
- A) Heisenberg's uncertainty principle states that it is impossible to simultaneously determine with perfect accuracy both the position and momentum of a particle. It is not related to the quantum numbers of electrons in an atom.
- B) Aufbau principle (German for "building up" principle) states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher energy levels. It describes the order of filling orbitals but doesn't address the uniqueness of quantum numbers for individual electrons.
- C) Hund's rule of maximum multiplicity states that for a given electron configuration, the term with the maximum multiplicity has the lowest energy. This means that electrons will occupy degenerate orbitals singly with parallel spins before pairing up. It describes how electrons fill orbitals of the same energy but doesn't state that no two electrons can have the same set of all four quantum numbers.
