Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Equivalent energy of mass equal to 1 a.m.u. is?
Text Solution
Verified by ExpertsThe correct answer is:
C
Step 1: The atomic mass unit (a.m.u) is a standard unit of mass used in atomic and molecular physics. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state.
Step 2: The equivalent energy of mass can be calculated using Einstein's famous equation, $E = mc^2$, where:
- $E$ is the energy in joules,
- $m$ is the mass in kilograms,
- $c$ is the speed of light in vacuum (approximately $3 imes 10^8$ m/s).
Step 3: To find the energy equivalent of 1 a.m.u., we need to use the conversion factor for a.m.u. to kilograms: 1 a.m.u. is approximately $1.66 imes 10^{-27}$ kg.
Step 4: Substitute the values into the equation:
$$E = (1.66 imes 10^{-27} ext{ kg}) imes (3 imes 10^8 ext{ m/s})^2$$
$$E ext{ (in joules)} = 1.66 imes 10^{-27} imes 9 imes 10^{16} = 1.494 imes 10^{-10} ext{ J}$$
Step 5: To convert joules to electronvolts (eV), we use the conversion $1 ext{ eV} = 1.6 imes 10^{-19} ext{ J}$. Therefore,
$$E ext{ (in eV)} = \frac{1.494 imes 10^{-10}}{1.6 imes 10^{-19}} ext{ eV} ext{ (calculating)}$$
$$E ext{ (in eV)} \approx 931.5 ext{ MeV}$$
Step 6: Rounding this gives us approximately 931 MeV.
Therefore, the correct answer is Option C: 931 MeV.
Step 2: The equivalent energy of mass can be calculated using Einstein's famous equation, $E = mc^2$, where:
- $E$ is the energy in joules,
- $m$ is the mass in kilograms,
- $c$ is the speed of light in vacuum (approximately $3 imes 10^8$ m/s).
Step 3: To find the energy equivalent of 1 a.m.u., we need to use the conversion factor for a.m.u. to kilograms: 1 a.m.u. is approximately $1.66 imes 10^{-27}$ kg.
Step 4: Substitute the values into the equation:
$$E = (1.66 imes 10^{-27} ext{ kg}) imes (3 imes 10^8 ext{ m/s})^2$$
$$E ext{ (in joules)} = 1.66 imes 10^{-27} imes 9 imes 10^{16} = 1.494 imes 10^{-10} ext{ J}$$
Step 5: To convert joules to electronvolts (eV), we use the conversion $1 ext{ eV} = 1.6 imes 10^{-19} ext{ J}$. Therefore,
$$E ext{ (in eV)} = \frac{1.494 imes 10^{-10}}{1.6 imes 10^{-19}} ext{ eV} ext{ (calculating)}$$
$$E ext{ (in eV)} \approx 931.5 ext{ MeV}$$
Step 6: Rounding this gives us approximately 931 MeV.
Therefore, the correct answer is Option C: 931 MeV.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Which of the following particles are constituents of the nucleus?
The particles which can be added to the nucleus of an atom without changing its chemical properties…
The neutron was discovered by
The energy equivalent of 1 kilogram of matter is about
Nuclear binding energy is equivalent to
If the binding energy of the deutrium is 2.23 MeV. The mass defect given in a.m.u. is