The binding energy of 20 10 Ne is 161 MeV. Find its atomic mass.

To find the atomic mass of an isotope, you need to know the number of protons and neutrons in its nucleus. In this case, Neon-20 (₁₀ Ne) has an atomic number of 10, which means it has 10 protons.

To determine the number of neutrons, you can subtract the atomic number from the atomic mass number. The atomic mass number is the sum of the protons and neutrons. Since the binding energy is given, you can assume that it represents the energy required to remove all the nucleons (protons and neutrons) from the nucleus of an atom.

The binding energy is the difference between the total energy of the separate nucleons and the energy of the nucleus. It is usually expressed in MeV (million electron volts). The binding energy is related to the mass defect, which is the difference between the mass of the nucleus and the sum of the masses of its constituent particles.

The relationship between binding energy (BE) and mass defect (Δm) is given by Einstein's mass-energy equation: E = Δmc², where c is the speed of light. Since the speed of light is a very large number, the binding energy can be approximated using the equation:

BE ≈ Δmc²

Given that the binding energy of Neon-20 is 161 MeV, we can use this equation to estimate the mass defect:

161 MeV ≈ Δmc²

Now, we need to convert the binding energy from MeV to kg, as the speed of light is measured in meters per second (m/s) and mass is measured in kilograms (kg). We know that 1 MeV is equivalent to 1.6 x 10⁻¹³ joules (J).

1 MeV = 1.6 x 10⁻¹³ J

To convert the binding energy from MeV to J, we multiply it by the conversion factor:

161 MeV × (1.6 x 10⁻¹³ J / 1 MeV) = 2.576 x 10⁻¹² J

Now, we can rearrange Einstein's mass-energy equation to solve for the mass defect (Δm):

BE ≈ Δmc²
2.576 x 10⁻¹² J ≈ Δm (kg) × (3.0 x 10⁸ m/s)²

Simplifying the equation:

Δm = (2.576 x 10⁻¹² J) / [(3.0 x 10⁸ m/s)²]

Calculating:

Δm ≈ 2.862 x 10⁻²⁷ kg

The mass defect represents the combined mass of the protons and neutrons that are tightly bound together in the nucleus. To calculate the atomic mass, we need to add the mass defect to the number of protons (atomic number):

Atomic mass = Number of protons (atomic number) + Mass defect

Atomic mass = 10 + 2.862 x 10⁻²⁷ kg

Thus, the atomic mass of Neon-20 (₁₀ Ne) is approximately 10 + 2.862 x 10⁻²⁷ kg.