Tungsten is a rare metal found naturally on earth almost exclusively combined with other elements in chemical compounds as opposed to on its own. Tungsten alloys have many applications including X-ray tubes, light bulb filaments and radiation shielding. The four most abundant isotopes of tungsten are: 180W, 182W, 183W, and 184W. Determine the number of protons, electrons and neutrons in each isotope. If a neutron has a mass of 1.67 x 10-27 kg, what is the total mass of neutrons (in grams) in Tungsten
The Correct Answer and Explanation is :
Number of Protons, Electrons, and Neutrons in Tungsten Isotopes:
Tungsten (W) has an atomic number of 74, meaning every isotope of tungsten has:
- 74 protons (since the number of protons defines the element)
- 74 electrons (since atoms are electrically neutral)
The number of neutrons varies depending on the isotope. The number of neutrons is determined using:
[
\text{Neutrons} = \text{Mass Number} – \text{Protons}
]
For each isotope:
- ( ^{180}W ): ( 180 – 74 = 106 ) neutrons
- ( ^{182}W ): ( 182 – 74 = 108 ) neutrons
- ( ^{183}W ): ( 183 – 74 = 109 ) neutrons
- ( ^{184}W ): ( 184 – 74 = 110 ) neutrons
Total Mass of Neutrons in Tungsten:
A single neutron has a mass of ( 1.67 \times 10^{-27} ) kg. Converting to grams:
[
1.67 \times 10^{-27} \times 10^{3} = 1.67 \times 10^{-24} \text{ g}
]
To find the total mass of neutrons in one mole of tungsten, we need the weighted average number of neutrons per tungsten atom. The natural abundances of these isotopes are approximately:
- ( ^{180}W ) = 0.12%
- ( ^{182}W ) = 26.50%
- ( ^{183}W ) = 14.30%
- ( ^{184}W ) = 30.64%
- ( ^{186}W ) = 28.43% (excluded since it’s not part of the four mentioned)
Using a weighted average:
[
\text{Avg. neutrons} = (106 \times 0.0012) + (108 \times 0.265) + (109 \times 0.143) + (110 \times 0.3064)
]
[
= 0.1272 + 28.62 + 15.587 + 33.704
]
[
\approx 107.9 \text{ neutrons per atom}
]
Total neutron mass per mole (using Avogadro’s number, ( 6.022 \times 10^{23} )):
[
(107.9) \times (1.67 \times 10^{-24} \text{ g}) \times (6.022 \times 10^{23})
]
[
= 1.09 \times 10^2 \text{ g}
]
So, the total neutron mass in one mole of tungsten is approximately 109 g.
Now, let me generate the image.
Here is the scientific infographic illustrating the four most abundant isotopes of tungsten, their atomic structures, and neutron mass calculations. Let me know if you need any modifications!