Equivalent energy of mass equal to 1 amu is…A… and rest energy of an electron is …B… Here A and B refer to

Options

A. `913 keV, 10 MeV`
B. `931 eV, 931 MeV`
C. `931.5 MeV, 510 keV`
D. `931 MeV, 931 KeV`

Answer

To solve the problem, we need to find the equivalent energy of mass equal to 1 amu (A) and the rest energy of an electron (B).

### Step-by-Step Solution:

**Step 1: Calculate the equivalent energy of 1 amu (A)**
1. The mass of 1 atomic mass unit (amu) is approximately \(1.66 \times 10^{-27}\) kg.
2. According to Einstein's mass-energy equivalence principle, the energy (E) can be calculated using the formula:
\[ E = mc^2 \]
where \(m\) is the mass and \(c\) is the speed of light in vacuum, which is approximately \(3 \times 10^8\) m/s.
3. Plugging in the values:
\[ E = (1.66 \times 10^{-27} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]
4. Calculating \(c^2\):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]
5. Now substituting back into the energy equation:
\[ E = 1.66 \times 10^{-27} \times 9 \times 10^{16} = 1.494 \times 10^{-10} \text{ J} \]
6. To convert this energy into mega electron volts (MeV), we use the conversion factor \(1 \text{ J} = 6.242 \times 10^{12} \text{ MeV}\):
\[ E \approx 1.494 \times 10^{-10} \text{ J} \times 6.242 \times 10^{12} \text{ MeV/J} \approx 931.5 \text{ MeV} \]
So, \(A = 931.5 \text{ MeV}\).

**Step 2: Calculate the rest energy of an electron (B)**
1. The mass of an electron is approximately \(9.1 \times 10^{-31}\) kg.
2. Using the same energy formula \(E = mc^2\):
\[ E = (9.1 \times 10^{-31} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]
3. Again, we use \(c^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2\):
\[ E = 9.1 \times 10^{-31} \times 9 \times 10^{16} = 8.19 \times 10^{-14} \text{ J} \]
4. Converting this energy into kilo electron volts (keV):
\[ E \approx 8.19 \times 10^{-14} \text{ J} \times 6.242 \times 10^{12} \text{ MeV/J} \approx 0.511 \text{ MeV} \approx 510 \text{ keV} \]
So, \(B = 510 \text{ keV}\).

### Final Answers:
- \(A = 931.5 \text{ MeV}\)
- \(B = 510 \text{ keV}\)