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Chapter 15: Problem 19

To illustrate the principle, let's say we start with a nucleus whose mass is \(200.000\) a.m.u. and inject \(1,600 \mathrm{MeV}\) of energy to completely dismantle the nucleus into its constituent parts. How much mass would the final collection of parts have? a) the exact same: \(200.000\) a.m.u. b) less than \(200.000\) a.m.u. c) more than \(200.000\) a.m.u.

Short Answer

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Question: After injecting a certain amount of energy to dismantle a nucleus, the mass of the final collection of parts is: a) the exact same: 200.000 a.m.u. b) less than 200.000 a.m.u. c) more than 200.000 a.m.u. Please provide the initial mass of the nucleus and the energy injected in MeV.

Step by step solution

01

Understand the mass-energy equivalence formula

The mass-energy equivalence formula, E=mc^2, states that energy (E) is equal to the mass (m) multiplied by the speed of light (c) squared. In this exercise, we are given the energy injected into the nucleus, and we will use this formula to find out the change in mass.
02

Convert the given energy to a.m.u.

The energy given is in \(\mathrm{MeV}\), and we need to convert it to atomic mass units (a.m.u.). First, we need to convert \(\mathrm{MeV}\) to Joules using the conversion factor 1 \(\mathrm{MeV} = 1.602\times10^{-13}\,\mathrm{J}\). Then, we can convert Joules to a.m.u. using the conversion factor 1 a.m.u. = 931.5 \(\mathrm{MeV/c^2}\).
03

Find the change in mass

As we have the energy in a.m.u. now, we can use the mass-energy equivalence formula to find the change in mass: \(\Delta m = \dfrac{E}{c^2}\).
04

Determine the final mass

Add the change in mass to the initial mass (200.000 a.m.u.) to find the final mass of the constituent parts.
05

Compare the final mass to the initial mass

Based on the final mass obtained in Step 4, choose the correct answer among the options a) the exact same: 200.000 a.m.u., b) less than 200.000 a.m.u., or c) more than 200.000 a.m.u.

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