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Ch 37: The Foundations of Modern Physics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경
37장, 문제 45b

To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter ¹²C nucleus. The proton must impact the nucleus with a kinetic energy of 3.00 MeV. Assume the nucleus remains at rest. Through what potential difference must the proton be accelerated from rest to acquire this speed?

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Determine the relationship between the kinetic energy of the proton and the potential difference it must be accelerated through. The work-energy principle states that the work done on the proton by the electric field is equal to its kinetic energy. This can be expressed as: K = q \(\cdot\) \(\Delta\) V, where K is the kinetic energy, q is the charge of the proton, and \(\Delta\) V is the potential difference.
Rearrange the formula to solve for the potential difference: \(\Delta\) V = \(\frac{K}{q}\). Here, K = 3.00 \ \(\text{MeV}\) (convert this to joules for consistency in SI units), and q is the charge of the proton, which is 1.602 \(\times\) 10^{-19} \ \(\text{C}\).
Convert the kinetic energy from MeV to joules. Use the conversion factor 1 \ \(\text{MeV}\) = 1.602 \(\times\) 10^{-13} \ \(\text{J}\). Multiply 3.00 \ \(\text{MeV}\) by this factor to get the kinetic energy in joules.
Substitute the values of K (in joules) and q (in coulombs) into the formula \(\Delta\) V = \(\frac{K}{q}\) to calculate the potential difference.
Ensure the units are consistent and verify the calculation. The resulting potential difference will be in volts, which represents the energy per unit charge required to accelerate the proton to the given kinetic energy.

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주요 개념

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Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In nuclear physics, the kinetic energy of particles like protons is crucial for understanding their ability to overcome potential barriers, such as the Coulomb barrier in nuclear reactions.
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가이드 코스
06:07
Intro to Rotational Kinetic Energy

Potential Difference

Potential difference, or voltage, is the work done per unit charge to move a charge between two points in an electric field. It is directly related to the kinetic energy gained by a charged particle when accelerated through an electric field, expressed as KE = qV, where q is the charge and V is the potential difference.
추천 영상:
가이드 코스
07:04
Potential Difference Between Two Charges

Coulomb Barrier

The Coulomb barrier is the energy barrier due to electrostatic repulsion that charged particles must overcome to get close enough for nuclear reactions to occur. In this context, the proton must have sufficient kinetic energy to overcome this barrier to successfully impact the nucleus of the carbon atom.
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