Question

The mass of a proton is 1.00728 amu and that of a neutron is 1.00867 amu. What is the mass defect (in amu) of a Ni nucleus? (The mass of a nickel- 60 nucleus is 59.9308 amu.)

Answer 1

The mass defect of a nickel-60 nucleus is calculated by subtracting the actual nucleus mass from the combined masses of its protons and neutrons. The actual nucleus mass is 59.9308 amu, while the combined mass of protons and neutrons is 60.4828 amu, resulting in a mass defect of 0.5520 amu.

Step-by-step explanation:

The mass defect of a nucleus is the difference between the combined mass of the protons and neutrons in a nucleus and the actual mass of the nucleus. In the case of a nickel-60 nucleus, which consists of 28 protons and 32 neutrons (since the mass number of nickel-60 is 60 and the atomic number of nickel is 28), we would expect the mass to be (28 x 1.0073 amu for protons) + (32 x 1.0087 amu for neutrons). However, the actual mass is given as 59.9308 amu.

To calculate the mass defect, we first calculate the expected mass, which is (28 x 1.0073 amu) + (32 x 1.0087 amu), and then subtract the actual mass of the nucleus:

Mass defect = [(28 x 1.0073 amu) + (32 × 1.0087 amu)] - 59.9308 amu

Lets calculate the expected mass:

Expected mass = (28 x 1.0073 amu) + (32 x 1.0087 amu) = 28.2044 amu + 32.2784 amu = 60.4828 amu

Now, subtract the actual mass of the nucleus from the expected mass to find the mass defect:

Mass defect = 60.4828 amu - 59.9308 amu = 0.5520 amu

The mass defect for a nickel-60 nucleus is therefore 0.5520 amu.

Answer 2

Mass Defect: 0.5505 amu.

Explanation

A nickel-60 atom contains sixty nucleons (neutrons and protons).

• Nickel has atomic number 28 as seen on a periodic table. 28 out of the 60 nucleons are thus protons.
• The rest of the 60 - 28 = 32 nucleons are, therefore, neutrons.

According to the question,

• each proton has a mass of 1.00728 amu. 28 of them shall have a mass of
  `28 * 1.00728  = 28.20384\; \text{amu}`;
• each neutron has a mass of 1.00867 amu. 32 of them shall have a mass of
  `32 * 1.00867 = 32.27744 \; \text{amu}`.

Mass of the 60 nucleons shall add up to
`28.20384 + 32.27744 = 60.48128 \; \text{amu}`.

The mass defect of a nucleus is "the difference between the sum of masses of [its] components and [its] measured [mass]." ("Map: A Molecular Approach (Tro)", Chemistry Libretexts)

According to the question, the measured mass of a nickel-60 nucleus is 59.9308 amu.

The difference between the sum of the masses of its nucleon components and the mass of its nucleus is, therefore,
`60.48128 - 59.9308 = 0.5505\;\text{amu}` (accurate to four decimal places.)