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Mobile App Chapter 2: Problem 3
The ratio of specific charge óf a proton and an \(\alpha\) -particle is (a) \(2: 1\) (b) \(1: 2\) (c) \(1: 4\) (d) \(1: 1\)
Short Answer
Expert verified
The ratio of specific charge of a proton and an \(\alpha\)-particle is \(1:2\).
Step by step solution
01
Understanding the Concept of Specific Charge
The specific charge of a particle is the ratio of its charge to its mass. For a proton, the charge is +1e (where e is the elementary charge, approximately equal to 1.602 x 10^-19 coulombs) and the mass is approximately 1.672 x 10^-27 kilograms. For an \(\alpha\)-particle, which is a helium nucleus, the charge is +2e (twice that of a proton since it contains two protons) and the mass is approximately 4 times that of a proton, given its two protons and two neutrons.
02
Calculating the Specific Charge for both Particles
Calculate the specific charge for the proton (\textbackslash(sigma_{\text{proton}})) and the \(\alpha\)-particle (\textbackslash(sigma_{\alpha})) using the formula \textbackslash(sigma = \frac{q}{m}) where q is the charge and m is the mass. For the proton, \(\textbackslash(sigma_{\text{proton}} = \frac{+1e}{1 u}\). For the \(\alpha\)-particle, \(\textbackslash(sigma_{\alpha} = \frac{+2e}{4 u}= \frac{+1e}{2 u}\).
03
Comparing the Specific Charges
To determine the ratio of specific charge, we divide the specific charge of the proton by that of the \(\alpha\)-particle: \(\frac{\textbackslash(sigma_{\text{proton}})}{\textbackslash(sigma_{\alpha})} = \frac{\frac{+1e}{1 u}}{\frac{+1e}{2 u}}\).
04
Simplifying the Ratio
When we simplify the ratio, we find that the 1 u in the numerator and the 2 u in the denominator indicate the mass ratio while the elementary charges cancel out, leaving us with \(\frac{1 u}{2 u}\), which simplifies to \(1:2\). Thus, the ratio of the specific charge of a proton to an \(\alpha\)-particle is \(1:2\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Physical Chemistry
Physical chemistry lies at the intersection of chemistry and physics, focusing on understanding the physical properties of molecules, the forces that act upon them, and the energy dynamics during chemical reactions. A critical aspect of physical[-]chemistry is the study of the specific charge of subatomic particles, which is a fundamental concept in elucidating the behavior of ions and nuclei under the influence of electric and magnetic fields.
The exercise in question explores the specific charge ratio, which reflects how different particles respond to electromagnetic fields. In physical chemistry, grasping such concepts is crucial for topics ranging from spectroscopy to quantum mechanics and thermodynamics. Knowing how to compare the specific charges of different particles is essential for interpreting experimental data and predicting the outcomes of chemical reactions that involve charged species.
The exercise in question explores the specific charge ratio, which reflects how different particles respond to electromagnetic fields. In physical chemistry, grasping such concepts is crucial for topics ranging from spectroscopy to quantum mechanics and thermodynamics. Knowing how to compare the specific charges of different particles is essential for interpreting experimental data and predicting the outcomes of chemical reactions that involve charged species.
Proton and Alpha-Particle
Diving deeper into the nitty-gritty of subatomic particles, let's talk about protons and alpha-particles. Protons are positively charged particles found within the nucleus of an atom. They have a unique charge of +1e, where e is the elementary charge. Proton's mass is one of the defining factors of an atom's identity and forms the basis of the chemical element's atomic number.
On the other side, an alpha-particle, also known as a helium nucleus, is composed of two protons and two neutrons. Its charge is therefore +2e due to the two protons. Its mass is approximately four times that of a single proton because it includes not just the two protons but also the two neutrons, which have a comparable mass to protons. The specific charge, which is the charge-to-mass ratio, is critical for these particles as it dictates their trajectory in a magnetic or electric field - a principle widely used in particle accelerators and various forms of mass spectrometry.
On the other side, an alpha-particle, also known as a helium nucleus, is composed of two protons and two neutrons. Its charge is therefore +2e due to the two protons. Its mass is approximately four times that of a single proton because it includes not just the two protons but also the two neutrons, which have a comparable mass to protons. The specific charge, which is the charge-to-mass ratio, is critical for these particles as it dictates their trajectory in a magnetic or electric field - a principle widely used in particle accelerators and various forms of mass spectrometry.
JEE Chemistry Preparation
For students undertaking the Joint Entrance Examination (JEE) in India, mastering concepts like specific charge ratios is highly significant. JEE chemistry preparation involves a balanced focus on physical, organic, and inorganic chemistry, and within physical chemistry, understanding the behavior of particles like protons and alpha-particles under various fields is a must.
The JEE syllabus requires a thorough preparation strategy that emphasizes conceptual clarity and problem-solving speed. Questions, such as comparing specific charge ratios, are typical in the examination, demanding students be adept at swift calculations and clear in their understanding of fundamental principles. Strengthening your concepts about subatomic particles, their interactions, and their role in chemical reactions can provide a substantial advantage in acing the physical chemistry section of the JEE.
The JEE syllabus requires a thorough preparation strategy that emphasizes conceptual clarity and problem-solving speed. Questions, such as comparing specific charge ratios, are typical in the examination, demanding students be adept at swift calculations and clear in their understanding of fundamental principles. Strengthening your concepts about subatomic particles, their interactions, and their role in chemical reactions can provide a substantial advantage in acing the physical chemistry section of the JEE.
