Question 158: Atoms & Nuclei

Question

The energy equivalent of $$1 \mathrm{~g}$$ of substance is :

Accepted Answer

To determine the energy equivalent of a mass, we use Einstein's mass-energy equivalence principle given by the equation:
$$E = mc^2$$
where:
- $$E$$ is the energy
- $$m$$ is the mass
- $$c$$ is the speed of light in a vacuum, which is approximately $$3 	imes 10^8 \mathrm{~m/s}$$
Given the mass $$m = 1 \mathrm{~g} = 1 	imes 10^{-3} \mathrm{~kg}$$, we can substitute these values into the equation:
$$E = (1 	imes 10^{-3} \mathrm{~kg}) 	imes (3 	imes 10^8 \mathrm{~m/s})^2$$
Calculating this, we get:
$$E = 1 	imes 10^{-3} 	imes 9 	imes 10^{16}$$
$$E = 9 	imes 10^{13} \mathrm{~J}$$
Next, to convert this energy into electron volts ($$\mathrm{eV}$$), we use the conversion factor: $$1 \mathrm{~J} = 6.242 	imes 10^{12} \mathrm{~MeV}$$.
Therefore:
$$E = 9 	imes 10^{13} \mathrm{~J} 	imes 6.242 	imes 10^{12} \mathrm{~MeV/J}$$
Calculating this, we get:
$$E = 5.6178 	imes 10^{26} \mathrm{~MeV}$$
Therefore, the energy equivalent of $$1 \mathrm{~g}$$ of a substance is:
Option A:
$$5.6 	imes 10^{26} \mathrm{~MeV}$$

Answer

$$5.6 	imes 10^{26} \mathrm{~MeV}$$

Answer

$$5.6 	imes 10^{12} \mathrm{~MeV}$$

Answer

$$5.6 \mathrm{~eV}$$

Answer

$$11.2 	imes 10^{24} \mathrm{~MeV}$$

Atoms & Nuclei

The energy equivalent of $1 \mathrm{~g}$ of substance is :

Choose the correct answer: