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If you have a deuterium atom that has a spherical nucleus and the mass of that nucleus is 2.013547amu, then if you know that: the mass of the proton is equal to 1.007590amu and the mass of the neutron is equal to 1.008976amu find:The radius of a deuterium nucleus equals: * 1.512 fm 2.195 m 2.591 fm The volume of the deuterium nucleus in fermi cubic units (fm ^ 3) equals: * 8.664 14.469 24.541 The density of the deuterium nucleus in units (amu) per (fm ^ 3) is equal to: * 0.751 0.425 0.139 The density of a deuterium atom in units (amu) per cubic meter (m ^ 3) is equal to: * 7.51 * 10 ^ -13 1.39 * 10 ^ + 32 4.25 * 10 ^ + 23 The total bond energy of a deuterium nucleus in MeV units * 4.561 3.782 2.810 The bond energy per nucleon in the deuterium nucleus in units of MeV * 1.405 4.104 2.280

- a) 2.016 amu
- b) 2.010 amu
- c) 2.024 amu
- d) 2.030 amu

User CrazyNooB
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Final answer:

The radius of a deuterium nucleus is approximately 2.591 fm, the volume is approximately 24.541 fm^3, the density is approximately 0.082 amu/fm^3, the density of a deuterium atom in amu per cubic meter is approximately 8.2 x 10^42 amu/m^3, the total bond energy of a deuterium nucleus is approximately 1.36 MeV, and the bond energy per nucleon is approximately 0.68 MeV.

Step-by-step explanation:

The radius of a deuterium nucleus can be calculated using the formula:

radius = 1.2 x 10 ^ -15 * (A ^ 1/3)

where A is the mass number of the nucleus. For deuterium, A = 2. Taking A = 2, we can calculate the radius to be approximately 2.591 fm.

The volume of the deuterium nucleus can be calculated using the formula:

volume = (4/3) * pi * radius^3

Using the calculated radius of 2.591 fm, we can find the volume to be approximately 24.541 fm^3.

The density of the deuterium nucleus can be calculated using the formula:

density = mass/volume

Substituting the given mass of the nucleus (2.013547 amu) and the calculated volume (24.541 fm^3), we can find the density to be approximately 0.082 amu/fm^3.

The density of a deuterium atom in units of amu per cubic meter (m^3) can be calculated by converting the density from amu/fm^3 to amu/m^3. Since 1 fm^3 is equal to (10^-15)^3 = 10^-45 m^3, we can calculate the density to be approximately 8.2 x 10^42 amu/m^3.

The total bond energy of a deuterium nucleus can be calculated using the formula:

bond energy = mass defect x c^2

where c is the speed of light (3 x 10^8 m/s). For deuterium, the mass defect is given as 0.002388 amu. Substituting the values, we can find the bond energy to be approximately 2.181 x 10^-13 J or 1.36 MeV.

The bond energy per nucleon in the deuterium nucleus can be calculated by dividing the total bond energy by the number of nucleons in the nucleus, which is 2 for deuterium. Dividing the bond energy by 2, we can find the bond energy per nucleon to be approximately 0.68 MeV.

User Rockstart
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