Question

Вычислите дефект массы и энергию связи ядра бора , если масса атома бора равна 11,009305 а. е. м.,масса атома водорода равна 1,007825 а. е. м., масса нейтрона — 1,008665 а. е. м. В ответе долго получиться 1,36*10-28 кг и 1,22*10-11 Дж, нужно решение, пожалуйста!!!

Answer 1

Calculation of Mass Defect and Binding Energy of Boron Nucleus

To calculate the mass defect and binding energy of the boron nucleus, we need to consider the masses of the individual particles involved: the boron atom, hydrogen atom, and neutron.

Given: - Mass of boron atom (B) = 11.009305 amu (atomic mass units) - Mass of hydrogen atom (H) = 1.007825 amu - Mass of neutron (n) = 1.008665 amu

Mass Defect Calculation:

The mass defect (Δm) is the difference between the mass of the nucleus and the sum of the masses of its individual particles. It is calculated using the formula:

Δm = (Z * mp + N * mn) - M

Where: - Z is the number of protons in the nucleus (atomic number) - N is the number of neutrons in the nucleus - mp is the mass of a proton - mn is the mass of a neutron - M is the mass of the nucleus

In the case of boron (B), the atomic number (Z) is 5, and the number of neutrons (N) is 6.

Using the given masses of the particles, we can calculate the mass defect:

Δm = (5 * mp + 6 * mn) - M

Binding Energy Calculation:

The binding energy (E) of a nucleus is the energy required to completely separate its nucleons (protons and neutrons) from each other. It is related to the mass defect by Einstein's famous equation:

E = Δm * c^2

Where: - E is the binding energy - Δm is the mass defect - c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s)

Using the calculated mass defect, we can now calculate the binding energy of the boron nucleus.

Let's perform the calculations:

Mass Defect Calculation:

Using the given masses of the particles, we can calculate the mass defect:

Δm = (5 * 1.007276 + 6 * 1.008665) - 11.009305

Calculating this expression, we find that the mass defect (Δm) is approximately 0.0678 amu.

Binding Energy Calculation:

Using Einstein's equation, we can calculate the binding energy:

E = Δm * c^2

Substituting the values:

E = 0.0678 * (3.00 x 10^8)^2

Calculating this expression, we find that the binding energy (E) is approximately 6.03 x 10^14 J (joules).

Therefore, the mass defect of the boron nucleus is approximately 0.0678 amu, and the binding energy is approximately 6.03 x 10^14 J.

Please note that the values provided are approximations and may vary slightly depending on the exact values used for the masses of the particles.