Answer: To determine the number of neutrons in a bromine nucleus, we first need to find the atomic number of bromine, which is the number of protons in its nucleus. The atomic number of bromine (Br) is 35, as indicated by its position in the periodic table.
Next, we find the mass number of bromine, which is the sum of protons and neutrons in the nucleus. The mass number is usually denoted by 'A'.
Now, we can calculate the number of neutrons (N) in the bromine nucleus using the formula:
N = A - Z
where:
N = number of neutrons
A = mass number
Z = atomic number (number of protons)
The mass number of bromine can be determined from its atomic weight, which is approximately 79.904 g/mol.
Now, let's calculate the number of neutrons:
Convert the given radius to femtometers (1 fm = 1 × 10^-15 m):
Radius = 5.06 × 10^-15 m = 5.06 fm
Calculate the volume of the nucleus (assuming a spherical nucleus):
Volume = (4/3) * π * (radius)^3
Calculate the density of the nucleus:
Density = Mass / Volume
Determine the mass of the nucleus using the atomic weight of bromine:
Mass = Atomic weight (in grams) / Avogadro's number (1 mole of atoms = 6.022 × 10^23 atoms)
Calculate the number of neutrons using the formula N = A - Z.
Let's proceed with the calculations:
Step 1: Convert the radius to femtometers
Radius = 5.06 × 10^-15 m = 5.06 fm
Step 2: Calculate the volume of the nucleus (assuming a spherical nucleus)
Volume = (4/3) * π * (5.06 fm)^3 ≈ 5.06 * 5.06 * 5.06 * (4/3) * π ≈ 539.45 fm³
Step 3: Calculate the density of the nucleus
Density = Mass / Volume
Step 4: Determine the mass of the nucleus using the atomic weight of bromine
Atomic weight of bromine (Br) ≈ 79.904 g/mol
Mass of the nucleus = Atomic weight (in grams) / Avogadro's number
Mass of the nucleus ≈ 79.904 g/mol / 6.022 × 10^23 mol^-1 ≈ 1.33 × 10^-22 g
Step 5: Calculate the number of neutrons using the formula N = A - Z
The atomic number of bromine (Br) = 35
Number of neutrons (N) = Mass number (A) - Atomic number (Z)
Number of neutrons (N) ≈ 79.904 - 35 ≈ 44.904
Therefore, there are approximately 44.904 neutrons in a bromine nucleus. Since neutrons must be whole numbers, the actual number of neutrons in a bromine nucleus is 45.