A beam of alpha particles is incident on a target of lead. A...

A beam of alpha particles is incident on a target of lead. A particular alpha particle comes in "head-on" to a particular lead nucleus and stops $6.50 \times 10^{-14} \mathrm{m}$ away from the center of the nucleus. This point is well outside the nucleus. Assume that the lead nucleus, which has 82 protons, remains at rest. The mass of the alpha particle is $6.64 \times 10^{-27}$ kg. (a) Calculate the electrostatic potential energy at the instant that the alpha particle stops. Express your result in joules and in MeV. (b) What initial kinetic energy (in joules and in MeV) did the alpha particle have? (c) What was the initial speed of the alpha particle?

Key Concepts

Coulomb's Law

Coulomb's law describes the force between two point charges and is fundamental to calculating the electrostatic interaction between charged particles. It states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is used to determine the potential energy between the interacting particles by integrating the force over distance.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored in a system of charges due to their positions relative to each other. For two point charges, it is calculated via the formula U = k · (q1 · q2) / r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the separation distance. This energy is key when analyzing interactions where kinetic energy is converted into potential energy, as in scattering events.

Conservation of Energy

The conservation of energy is a fundamental principle stating that the total energy of a closed system remains constant. In a collision or scattering event, the initial kinetic energy of a moving particle is converted into another form of energy, such as electrostatic potential energy at the turning point. This principle allows one to equate the initial kinetic energy with the potential energy at a specific position.

Kinetic Energy and Speed Relationship

Kinetic energy, the energy of motion for an object, is defined by the expression KE = (1/2)mv², where m is the mass and v is the velocity. In problems involving particle collisions or scattering, this relationship helps determine the initial speed once the kinetic energy is known. It also connects the dynamics of the motion to energy transformations.

Unit Conversion (Joules and MeV)

Unit conversion between joules and electronvolts (specifically mega-electronvolts, MeV) is essential in high-energy physics, where different scales of energy are used. Since 1 eV is the energy gained by an electron moving through a potential difference of 1 volt, and 1 MeV is 10^6 eV, converting energy values from joules (the SI unit) to MeV provides a more convenient scale for analyzing subatomic processes.

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