Question

For each of the questions, four choices have been provided. Select the correct alternative. If 20 electrons are present in the 4 th orbit then the atomic number of that element is (a) 58 (b) 59 (c) 56 (d) 60

Short answer

Short answer: The atomic number of this element is 48.

Step-by-step solution

Determine the maximum electrons in each orbital

To determine the number of electrons that can be present in each orbit (K, L, M, and N), we use the formula 2n². Here, n represents the given orbit. For K orbit (n = 1): 2(1²) = 2 electrons For L orbit (n = 2): 2(2²) = 8 electrons For M orbit (n = 3): 2(3²) = 18 electrons For N orbit (n = 4), we are given 20 electrons, but let's check the maximum capacity of the N orbit: 2(4²) = 32 electrons Since 20 electrons are less than the maximum capacity (32 electrons), it is valid.

Calculate the atomic number

The atomic number of an element is equal to the total number of electrons present in all the orbits. So, we need to add the electrons of K, L, M and N orbits to find the atomic number. K orbit: 2 electrons L orbit: 8 electrons M orbit: 18 electrons N orbit: 20 electrons Atomic number = 2 + 8 + 18 + 20 = 48 Since none of the given options has 48 as the atomic number, there might be a mistake in the problem or the given options.

Key concepts

Electron Configuration

Understanding electron configuration is essential for mastering the basics of chemistry. This concept describes how electrons are distributed in an element's orbitals, which are specific paths electrons follow around an atom's nucleus. The arrangement follows a set of rules known as the Pauli Exclusion Principle and Hund's Rule, ensuring that electrons occupy the lowest energy first before filling up higher energy levels.

For example, the first shell (K orbit) can hold up to 2 electrons, the second (L orbit) up to 8, and so on. Each orbit or energy level is further divided into sublevels known as s, p, d, and f. The electron configuration notation gives you precise information about the electrons in an atom, which is crucial for predicting the chemical behavior of elements.

Orbital Capacity

Orbital capacity refers to the maximum number of electrons a given energy level can hold, and this is determined by the formula 2n², where 'n' represents the principal quantum number or the orbit number (1 for K, 2 for L, etc.).

In simpler terms, the innermost orbit can hold up to 2 electrons, the next can hold up to 8, and it increases as you move to higher orbits. For example, as shown in the exercise: the fourth orbit, with n=4, can have a maximum of 32 electrons, based on the 2n² rule. Knowing these capacities is critical when determining the correct electron configuration and thus predicting an element's properties.

Chemistry Problem Solving

Effective chemistry problem-solving is much like a detective's work. It involves interpreting the given data correctly and applying the appropriate concepts and mathematical formulas. To solve a problem, one must carefully analyze each step and use deductive reasoning.

For instance, when calculating the atomic number from given electron configurations across orbits, one must accumulate the electrons from all orbits, applying the correct capacity rules. It's also important to note anomalies in the provided data, as they may hint at either a misprint or a concept that requires a deeper understanding. Therefore, attention to detail and a systematic approach are paramount.

Atomic Structure

The atomic structure is the arrangement of subatomic particles—protons, neutrons, and electrons—in an atom. The atomic number, symbolized as 'Z,' is one of the most crucial attributes of an element's atomic structure, indicating the number of protons in its nucleus. Since atoms are neutral, the number of protons equals the number of electrons.

An element's chemical properties are deeply rooted in its atomic structure, particularly the configuration of its electrons. The way these electrons are arranged in their various orbits determines how an element will react chemically with other elements. Understanding atomic structure is thus the cornerstone of not only chemistry but also related fields such as physics and materials science.