Question

In a naturally occurring sample, 19.8% of boron atoms have five neutrons and 80.2% have six neutrons. What is the mass number of each boron isotope? Sketch a sample of 10 atoms that is nearly representative of a natural sample. What is the average mass of the atoms in your drawing? What is the atomic mass of boron? (Boron-10 has a mass of 10.01294 amu and boron-11 has a mass of 11.00931 amu.)

Answer 1

Answer:

Mass of Boron with 5 neutrons = 10.07975 amu.

Mass of Boron with 6 neutrons = 11.08842 amu.

Average mass of the 10 atoms = 10.886686 amu.

Atomic mass of Boron = 10.81203 amu.

Explanation:

Boron has an atomic number equal to 5, so it has 5 protons in its nucleus. The mass number is given by the sum of the mass of protons and neutrons.

One proton has 1.00728 amu, and 1 neutron has 1.00867. So, the mass of the isotope which has 5 neutrons is:

Mass = 5x1.00728 + 5x1.00867 = 10.07975 amu

And the mass of the isotope with 6 neutrons is:

Mass = 5x1.00728 + 6x1.00867 = 11.08842 amu.

With 10 atoms of boron, 2 (19.8%) will have 5 neutrons and will have a mass equal to 10.07975 amu, and 8 (80.2%) will have 6 neutrons and mass equal to 11.08842 amu. So, the average mass is:

Average mass = (2x10.07975 + 8x11.08842)/10

Average mass = 10.886686 amu.

The atomic mass of Boron will be the average mass of its isotopes. So, for the mass of the isotope given, the atomic mass will be:

atomic mass = 0.198x10.01294 + 0.802x11.00931

atomic mass = 10.81203 amu.