The kilogram has been redefined based on Planck's constant (h) and a sphere of pure crystalline silicon: 8AsiVsphere Msphere = 2h 13 ст.а? The terms (with their relative uncertainties) are: (1) Planck's constant h (zero uncertainty as it is defined exactly); (2) the bracketed term including accurately known Rydberg constant R, speed of light c, mass of electron (me), and fine structure constant a, with a combined uncertainty of +4.7 × 10-8%; (3) atomic mass Asi for the 28 Si-enriched silicon (+5.4 x 10-7%); (4) volume of the Si sphere (+2.0 × 10-6%) and (5) crystal lattice parameter I (+1.84 x 10-7%). There are exactly eight atoms per unit cell in the sphere. Compute the relative uncertainty of msphere- To find the uncertainty of I, use the function y = x“, for which the uncertainty is propagated using %e, = a(%e,). relative uncertainty of msphere: % The mass of the sphere of pure silicon (999.698 336 5 g) must also be corrected for defects in the crystal lattice ( mdefects = 3.8 (±3.8) µg) and a surface oxide (moxide = 120.6 (+8.9) µg). msphere = msphere - mdefects + moxide What is the corrected mass (m'nbere) and associated absolute and relative uncertainty? m' 'sphere g
The kilogram has been redefined based on Planck's constant (h) and a sphere of pure crystalline silicon: 8AsiVsphere Msphere = 2h 13 ст.а? The terms (with their relative uncertainties) are: (1) Planck's constant h (zero uncertainty as it is defined exactly); (2) the bracketed term including accurately known Rydberg constant R, speed of light c, mass of electron (me), and fine structure constant a, with a combined uncertainty of +4.7 × 10-8%; (3) atomic mass Asi for the 28 Si-enriched silicon (+5.4 x 10-7%); (4) volume of the Si sphere (+2.0 × 10-6%) and (5) crystal lattice parameter I (+1.84 x 10-7%). There are exactly eight atoms per unit cell in the sphere. Compute the relative uncertainty of msphere- To find the uncertainty of I, use the function y = x“, for which the uncertainty is propagated using %e, = a(%e,). relative uncertainty of msphere: % The mass of the sphere of pure silicon (999.698 336 5 g) must also be corrected for defects in the crystal lattice ( mdefects = 3.8 (±3.8) µg) and a surface oxide (moxide = 120.6 (+8.9) µg). msphere = msphere - mdefects + moxide What is the corrected mass (m'nbere) and associated absolute and relative uncertainty? m' 'sphere g
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Transcribed Image Text:The kilogram has been redefined based on Planck's constant (h) and a sphere of pure crystalline silicon:
8AsiVsphere
Msphere = 2h
13
ст-а?
The terms (with their relative uncertainties) are: (1) Planck's constant h (zero uncertainty as it is defined exactly); (2) the
bracketed term including accurately known Rydberg constant R, speed of light c, mass of electron (me), and fine structure
constant a, with a combined uncertainty of +4.7 × 10-8%; (3) atomic mass Asi for the 28 Si-enriched silicon
(+5.4 x 10-7%); (4) volume of the Si sphere (+2.0 × 10-6%) and (5) crystal lattice parameter I (+1.84 x 10-7%). There are
exactly eight atoms per unit cell in the sphere.
Compute the relative uncertainty of myphere- To find the uncertainty of l, use the function y = x“, for which the uncertainty
is propagated using %e, = a(%e,).
relative uncertainty of msphere:
%
The mass of the sphere of pure silicon (999.698 336 5 g) must also be corrected for defects in the crystal lattice (
mdefects = 3.8 (±3.8) µg) and a surface oxide (moxide = 120.6 (+8.9) µg).
m'sphere
= msphere - mdefects + moxide
What is the corrected mass (mnhere) and associated absolute and relative uncertainty?
m'
g
'sphere
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