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Chapter 26: Problem 54

Find the conversion between the mass unit \(\mathrm{MeV} / c^{2}\) and the SI unit of mass.

Short Answer

Expert verified
#tag_title#Step 2: Use the mass-energy equivalence equation to find the mass in kilograms.#endregion#. #tag_content#Now that we have the energy in Joules, we can use Einstein's mass-energy equivalence equation, \(E = mc^2\), to find the corresponding mass in kilograms. Rearranging the equation to solve for mass, we get: \(m = \frac{E}{c^2}\) Here, E is the energy in Joules (1.60218 x 10^{-13} J) and c is the speed of light (2.99792 x 10^8 m/s). \( m = \frac{1.60218 \times 10^{-13} \,\mathrm{J}}{(2.99792 \times 10^8 \,\mathrm{m/s})^2} \\ m = 1.78266 \times 10^{-36} \,\mathrm{kg} \) Thus, we've found that a mass of 1 MeV/c² is equivalent to 1.78266 x 10^{-36} kg. #Step 3: Write the conversion equation. Now that we've found the conversion factor between MeV/c² and kg, we can express the conversion as an equation: 1 MeV/c² = 1.78266 x 10^{-36} kg. In summary, to convert a mass from MeV/c² to kilograms, simply multiply the mass in MeV/c² by the conversion factor above.

Step by step solution

01

Convert MeV to Joules#endregion#.

To convert Mega-electron Volts (MeV) to Joules (J), we need to use the conversion factor 1eV = 1.60218 x 10^{-19} J. Since we are dealing with MeV, we first need to express MeV in terms of eV: 1 MeV = 1 x 10^6 eV. Next, we'll convert eV to Joules using the conversion factor: 1 MeV = 1 x 10^6 eV x 1.60218 x 10^{-19} J/eV = 1.60218 x 10^{-13} J.

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