Converting Energy to Mass: Understanding the Relationship Between MeV and kg

In summary, the relationship between energy and mass is encapsulated in Einstein's equation E=mc², where energy (E) can be converted to mass (m) and vice versa. The concept of MeV (mega-electron volts) is a unit of energy commonly used in particle physics, and it can be converted to mass in kilograms using the equivalence factor derived from the speed of light (c). This relationship highlights how high-energy processes, such as those in nuclear reactions, can result in measurable changes in mass, illustrating the fundamental principle of mass-energy equivalence.
  • #1
Saibot
12
6
Homework Statement
Convert 1672 MeV/c^2 to kg
Relevant Equations
E=mc^2
(1672 MeV/c^2) * c^2 = 1.505 * 10^20 MeV = 1.505 * 10^26 eV = 2.41 * 10^7 J

Since E = mc^2, m = E/c^2

Therefore, m = 2.41 * 10^7 / (3 * 10^8)^2 = 2.68 * 10^-10 kg

But the answer is 2.97 * 10^-27 kg

Help! What is wrong with my logic?
 
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  • #2
##1~\text{eV} = 1.609 \times 10^{-19}~\text{J}##
eV is a unit of energy so eV/c2 is a unit of mass. Thus 1 J/c2 is kilograms. Conversely, if you multiply kilograms by c2 in (m/s)2, you get Joules.
Take it from there.
 
  • #3
Indeed, but if I directly convert 1672 MeV/c^2 using the fundamental charge:

(1672 * 10^6 eV/c^2) * 1.609 J/eV, I get 2.68 * 10^-10 J/c^2. This is kilograms.

Same wrong answer. I'm missing something here. I have to divide again by c^2 and I have no idea why.
 
  • #4
Saibot said:
(1672 MeV/c^2) * c^2 = 1.505 * 10^20 MeV
No. You haven't handled the conversion/units correctly. The 'c²'s (on the 'top' and the 'bottom') cancel, so the energy (in MeV) is 1672MeV.
 
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  • #5
OK, so it was incorrect to replace the "unit" c with the actual "value" of c (3*10^8). Got it, thanks mate.
 
  • #6
Saibot said:
(1672 * 10^6 eV/c^2) * 1.609 J/eV, I get 2.68 * 10^-10 J/c^2. This is kilograms.
Mind your units.

If ##~1~\text{eV} = 1.609 \times 10^{-19}~\text{J}##, ##~1~\text{J} = \frac{1}{1.609 \times 10^{-19}}~\text{eV}\implies 1~ \rm{J/eV}=6.21\times 10^{18}.##
 
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  • #7
Saibot said:
Therefore, m = 2.41 * 10^7 / (3 * 10^8)^2 = 2.68 * 10^-10 kg

But the answer is 2.97 * 10^-27 kg
You are off by a factor of ##\approx 9 \times 10^{16}##. This should give you a clue as to what you are doing wrong.
 
  • #8
Saibot said:
OK, so it was incorrect to replace the "unit" c with the actual "value" of c (3*10^8). Got it, thanks mate.
It's ok to replace the "unit" c with its actual value. But you didn't do it everwhere. So you should have done this:

##1672 MeV/c^2 \times c^2##

##= 1672 \times \frac {MeV}{(3 \times 10^8 m/s)^2} \times (3 \times 10^8 m/s)^2##

##= 1672MeV##

Of course, all that work is unnecesary once you understand that a mass of ##X~ MeV/c^2## is equivalent (using ##E=mc^2##) to an energy of ##X ~MeV##.
 
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  • #9
Understood. Thanks so much :)
 
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FAQ: Converting Energy to Mass: Understanding the Relationship Between MeV and kg

What is the basic principle behind converting energy to mass?

The basic principle behind converting energy to mass is derived from Einstein's famous equation \(E = mc^2\). This equation states that energy (E) and mass (m) are interchangeable; they are different forms of the same thing. The constant \(c\) represents the speed of light in a vacuum (approximately \(3 \times 10^8\) meters per second). This relationship allows us to calculate the mass equivalent of a given amount of energy.

How do you convert MeV to kilograms?

To convert Mega-electronvolts (MeV) to kilograms (kg), you can use the equation \(E = mc^2\). First, convert MeV to joules (J) using the conversion factor \(1 \text{ MeV} = 1.60218 \times 10^{-13} \text{ J}\). Then, rearrange the equation to solve for mass (\(m = \frac{E}{c^2}\)). For example, if you have 1 MeV of energy, the mass equivalent would be calculated as follows: \(1 \text{ MeV} = 1.60218 \times 10^{-13} \text{ J}\), and \(m = \frac{1.60218 \times 10^{-13} \text{ J}}{(3 \times 10^8 \text{ m/s})^2} \approx 1.78266 \times 10^{-30} \text{ kg}\).

Why is the conversion from MeV to kg important in physics?

The conversion from MeV to kg is important in physics because it allows scientists to understand and quantify the mass-energy equivalence in particle physics and nuclear reactions. This conversion is crucial for calculating the mass of subatomic particles, understanding binding energies in nuclei, and analyzing energy release in high-energy processes like nuclear fission and fusion.

What are some practical applications of converting energy to mass?

Practical applications of converting energy to mass include nuclear power generation, where the energy released from nuclear reactions is used to produce electricity. It is also essential in medical applications such as positron emission tomography (PET) scans, where the mass-energy equivalence principle helps in imaging and diagnosing diseases. Additionally, understanding this relationship is fundamental in particle physics research, such as in experiments conducted at particle accelerators like the Large Hadron Collider (LHC).

Are there any limitations or considerations when converting energy to mass?

There are several limitations and considerations when converting energy to mass. One limitation is the precision of the conversion factors and constants used, which can introduce small errors in calculations. Additionally, the conversion assumes a vacuum and does not account for

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