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Units and Measurement

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Question : 16 of 33
Marks: +1, -0
The unit of length convenient on the atomic scale is known as an angstrom and is denoted by A0:1 A0\overset{0}{A} : 1 \ \overset{0}{A} = 10−10^{-10} m. The size of a hydrogen atom is about 0.5 A0\overset{0}{A} . What is the total atomic volume in m3^{3} of a mole of hydrogen atoms?
Solution:  
Here, r=0.5 A0=0.5×10−10 mr=0.5 \ \overset{0}{A} =0.5 \times 10^{-10} \ \mathrm{m}
V1V_1= Volume of each hydrogen atom
=43Ï€r3= \frac{4}{3} \pi r^{3}
=43×3.14×(0.5×10−10)3= \frac{4}{3} \times 3.14 \times (0.5 \times 10^{-10})^{3}
=5.233×10−31 m3=5.233 \times 10^{-31} \ \mathrm{m}^{3}
According to Avogadro’s hypothesis, one mole of hydrogen contains:
N=6.023×1023N=6.023 \times 10^{23} atoms
∴\therefore Atomic volume of 1 mole of hydrogen atoms,
V=NV1V=N V_{1}
or V=6.023×1023×5.233×10−31V=6.023 \times 10^{23} \times 5.233 \times 10^{-31}
=3.152×10−7 m3≅3×10−7 m3=3.152 \times 10^{-7} \ \mathrm{m}^{3} \cong 3 \times 10^{-7} \ \mathrm{m}^{3}
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