If two deuterium nuclei (charge +e, mass 3.34×10−27kg) get close enough together, the attraction of the strong nuclear force wil
l fuse them to make an isotope of helium, releasing vast amounts of energy. The range of this force is about 10−15. This is the principle behind the fusion reactor. The deuterium nuclei are moving much too fast to be contained by physical walls, so they are confined magnetically. (a) How fast would two nuclei have to move so that in a head-on collision they would get close enough to fuse? (Assume their speeds are equal. Treat the nuclei as point charges, and assume that a separation of 1.0×10−15 is required for fusion.) (b) What strength magnetic field is needed to make deuterium nuclei with this speed travel in a circle of diameter 2.50 m?
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<u>Answer:</u> The average atomic mass of the given element is 20.169 amu.
<u>Explanation:</u>
Average atomic mass of an element is defined as the sum of masses of the isotopes each multiplied by their natural fractional abundance.
Formula used to calculate average atomic mass follows:
.....(1)
We are given:
- For isotope 1:
Mass of isotope 1 = 19.99 amu
Percentage abundance of isotope 1 = 90.92 %
Fractional abundance of isotope 1 = 0.9092
- For isotope 2:
Mass of isotope 2 = 20.99 amu
Percentage abundance of isotope 2 = 0.26%
Fractional abundance of isotope 2 = 0.0026
- For isotope 3:
Mass of isotope 3 = 21.99 amu
Percentage abundance of isotope 3 = 8.82%
Fractional abundance of isotope 3 = 0.0882
Putting values in equation 1, we get:
Hence, the average atomic mass of the given element is 20.169 amu.