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Q. 78

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 713

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Short Answer

A proton and an alpha particle are fired directly toward each other from far away, each with an initial speed of . What is their distance of closest approach, as measured between their centers?

The closest approach distance between a proton's center and an alpha particle is .

See the step by step solution

Step by Step Solution

Step 1. Given information and formulae used

Given:

Mass of proton,

Mass of an alpha particle,

Charge of proton,

Charge of alpha particle,

Initial velocity of both proton and alpha particle,

Formulae

We understand that the system's potential energy is

Here

are charges

is the permittivity

is the separation distance

The system's initial energy is kinetic energy.

Step 2.  How do you calculate the distance between a proton's center and an alpha particle's closest approach?

The kinetic energy of the system is calculated as

The particle will be closest when the entire kinetic energy will convert into potential energy

Plugging the values in the above equation

Distance of closest approach between the center of proton and an alpha particle is

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