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A alpha particle passes rapidly through the center of hydrogen molecule, moving on a line perpendicular to the internuclear axis. The distance between the nuclei is b. Where on its path does the alpha-particle experience the maximum force and what is it?
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A alpha particle passes rapidly through the center of hydrogen molecul...
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Introduction

When an alpha particle passes through the center of a hydrogen molecule on a line perpendicular to the internuclear axis, it experiences a force. In this case, we need to find out where on its path the alpha particle experiences the maximum force and what that force is.

Calculation

The force experienced by the alpha particle can be calculated using Coulomb's law. The electric force between two charged particles is given by:

F = k * q1 * q2 / r^2

Where F is the force, k is the Coulomb's constant, q1 and q2 are the charges on the particles, and r is the distance between them. In this case, the alpha particle has a charge of +2e, where e is the elementary charge. The hydrogen molecule consists of two protons, each with a charge of +e. Therefore, the force experienced by the alpha particle is:

F = k * (2e) * (+e) / (b/2)^2

Where b is the distance between the nuclei of the hydrogen molecule. At the point where the alpha particle is closest to the hydrogen nuclei, its distance from each proton is b/2. Therefore, we use b/2 as the distance between the alpha particle and each proton.

Maximum Force

To find the point where the alpha particle experiences the maximum force, we take the derivative of the force with respect to the distance between the nuclei, b. Setting the derivative equal to zero gives us the point of maximum force.

dF/db = -4k * (2e) * (+e) / (b^3) = 0

Solving for b, we get:

b = (8ke^2 / F)^(1/3)

Substituting this value of b into the expression for the force, we get:

F_max = k * (2e) * (+e) / [(8ke^2 / F)^(2/3)]

Simplifying this expression, we get:

F_max = (4 / 3) * (k * e^2 / b^2)

Therefore, the maximum force experienced by the alpha particle is:

F_max = (4 / 3) * (k * e^2 / b^2)

and it occurs at a distance of:

b = (8ke^2 / F)^(1/3)

Conclusion

In conclusion, when an alpha particle passes through the center of a hydrogen molecule on a line perpendicular to the internuclear axis, it experiences a force. The maximum force experienced by the alpha particle is given by:

F_max = (4 / 3) * (k * e^2 / b^2)

and it occurs at a distance of:

b = (8ke^2 / F)^(1/3)
Community Answer
A alpha particle passes rapidly through the center of hydrogen molecul...
B/2root2
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Similar Class 12 Doubts

A cyclotron is a kind of particle accelerator invented by Ernest O. Lawrence at the University of California, Berkeley, in 1929–1930, and patented in 1932. A cyclotron accelerates charged particles along a spiral path outward from the center. The particles are guided by a static magnetic field to a spiral trajectory, and accelerated by a rapidly changing electric field (radio frequency). For this invention Lawrence received the 1939 Nobel Prize in Physics.Cyclotrons were the most efficient particle accelerator equipment until the 1950s, when the synchrotron replaced them, and are now used in science and nuclear medicine to generate particle beams.This will toss the particle out of resonance with the oscillating field which means that when the particle reaches the hole between the dees, the extremity of the dees won't change. Thus, the particle won't be accelerated further.So, Cyclotron isn't reasonable for accelerating electrons. Because of the small mass, the speed of electrons increments quickly. Similarly, because of fast relativistic variation in their mass, the electrons escape step with the oscillating electric field.Hence, option A is the correct option.

A alpha particle passes rapidly through the center of hydrogen molecule, moving on a line perpendicular to the internuclear axis. The distance between the nuclei is b. Where on its path does the alpha-particle experience the maximum force and what is it?
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A alpha particle passes rapidly through the center of hydrogen molecule, moving on a line perpendicular to the internuclear axis. The distance between the nuclei is b. Where on its path does the alpha-particle experience the maximum force and what is it? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A alpha particle passes rapidly through the center of hydrogen molecule, moving on a line perpendicular to the internuclear axis. The distance between the nuclei is b. Where on its path does the alpha-particle experience the maximum force and what is it? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A alpha particle passes rapidly through the center of hydrogen molecule, moving on a line perpendicular to the internuclear axis. The distance between the nuclei is b. Where on its path does the alpha-particle experience the maximum force and what is it?.
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