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Chapter 2: Problem 3

How many number of electrons are present in a particle which carries a charge of \(5.5 \times 10^{-16} \mathrm{C} ?\) (a) 3432 (b) 1560 (c) 8240 (d) 2432

Short Answer

Expert verified
3432

Step by step solution

01

Understand the Problem

The problem asks to find out the number of electrons in a particle, given that the particle carries a charge of 5.5 x 10^-16 C.
02

Recall the Charge of a Single Electron

Recall that the charge of a single electron is approximately -1.602 x 10^-19 C (Coulombs).
03

Calculate the Number of Electrons

Divide the total charge by the charge of a single electron to find the number of electrons. Number of electrons = (Total charge) / (Charge of one electron).
04

Perform the Calculation

Substitute the given values into the equation: Number of electrons = (5.5 x 10^-16 C) / (-1.602 x 10^-19 C/electron). Take the absolute value since we are interested in the magnitude.
05

Obtain the Answer

Perform the calculation to get the number of electrons: Number of electrons ≈ 3432. The negative sign indicates the charge of the electrons and is not needed for the count.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number of Electrons
Understanding the basic units of matter is essential in chemistry, and one of those fundamental units is the electron. Electrons are subatomic particles with a negative charge, and they play a crucial role in the formation of atoms and molecules.

The number of electrons in an atom or a particle determines its electrical charge. Since atoms are electrically neutral, they must have an equal number of protons (positively charged particles) and electrons. However, when atoms gain or lose electrons, they become ions and carry a net charge.

When given the charge of a particle, one can determine the number of electrons it contains by using the elementary charge of an electron, which is approximately \text{-1.602 x \(10^{-19}\) C} (Coulombs). This is a key point to remember; the more accurately this value is retained, the more precise your calculations will be. For quantitative calculations, understanding that this negative charge represents a single electron will help you determine the electron count in charged particles or ions.

For example, if a particle has a charge of \text{5.5 x \(10^{-16}\) C}, dividing this by the elementary charge gives you the number of electrons that would collectively have the given charge, keeping in mind to consider the absolute value as the charge of electrons is negative by nature.
Coulomb's Law
Coulomb's Law is a fundamental principle in physics that describes the force of attraction or repulsion between two charged particles. Named after Charles-Augustin de Coulomb, the law quantifies the electrostatic force as directly proportional to the product of the electric charges of the particles and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is expressed as: \text{F = k \(\frac{|q1 x q2|}{r^2}\)}, where \text{F} is the force between the charges, \text{q1} and \text{q2} are the amounts of the charges, \text{r} is the distance between the centers of the two charges, and \text{k} is Coulomb's constant (\text{\(8.987 x 10^9\text{Nm}^2/\text{C}^2\)}). This fundamental law is used extensively for determining the electrostatic potential energy and force in systems of charged particles.

Understanding Coulomb's Law is critical for predicting how charged particles will interact within a field. It's also a key element in designing electric circuits, understanding molecular chemistry, and explaining the structural integrity of materials on a molecular level.
Quantitative Calculations in Chemistry
Quantitative calculations are at the heart of chemistry. They enable chemists to determine the amounts of substances required or yielded in a chemical reaction, and to make sense of experimental data. These calculations often involve moles, masses, volumes, concentrations, and energies.

One of the staples of quantitative chemistry is the mole concept, which provides a bridge between the atomic scale and the real-world scale, allowing the counting of particles by weighing. Another crucial concept is stoichiometry, which uses balanced chemical equations to determine the proportion of reactants and products.

For instance, in the exercise provided, we deal with quantitative calculation to find out the number of electrons based on the known charge. Applying the charge of a single electron and using simple division brings quantitative analysis into play to solve a practical problem in chemistry. Quantitative skills, when harnessed correctly, can unveil a wealth of information about chemical substances and their behaviors, making them instrumental for both theoretical and applied sciences.

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Most popular questions from this chapter

What will be the energy of a photon which corresponds to the wavelength of \(0.50 \mathrm{~A}\) ? (a) \(3.98 \times 10^{-15} \mathrm{~J}\) (b) \(3 \times 10^{15} \mathrm{~J}\) (c) \(3.9 \times 10^{8} \mathrm{~J}\) (d) \(3 \times 10^{-34} \mathrm{~J}\)

The emission spectrum of hydrogen is found to satisfy the expression for the energy change \(\Delta E\) (in joules) such that \(\Delta E=2.18 \times 10^{-18}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right) J\) where \(n_{1}=1,2,3, \ldots .\) and \(n_{2}=2,3,4\). The spectral lines corresponds to Paschen series if (a) \(n_{1}=1\) and \(n_{2}=2,3,4\) (b) \(n_{1}=3\) and \(n_{2}=4,5,6\) (c) \(n_{1}=1\) and \(n_{2}=3,4,5\) (d) \(n_{1}=2\) and \(n_{2}=3,4,5\)

How many subshells and electrons are associated with \(n=4\) ? (a) 32,64 (b) 16,32 (c) 4,16 (d) 8,16

The energy difference between the ground state of an atom and its excited state is \(3 \times 10^{-19} \mathrm{~J}\). What is the wavelength of the photon required for this transition? (a) \(6.6 \times 10^{-34} \mathrm{~m}\) (b) \(3 \times 10^{-8} \mathrm{~m}\) (c) \(1.8 \times 10^{-7} \mathrm{~m}\) (d) \(6.6 \times 10^{-7} \mathrm{~m}\)

Which of the following configurations represents a noble gas? (a) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 f^{14} 5 s^{2}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} 5 p^{6}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} 5 p^{3}\)
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