# Uncertainty, Signficant Figures, and Energy Diagrams

Find the absolute uncertainty of the following calculations and express the answer with the proper number of significant figures.

a) 2.0394 (Â± 0.0008) + 3.256 (Â± 0.004) - 1.17 (Â± 0.01) = ______________________________

b) 91.3 (Â± 0.5) * 40.03 (Â± 0.02) / 16.1 (Â± 0.3) = _____________________________________

c) [12.34 (Â± 0.04) - 7.453 (Â± 0.007)] / 18.4 (Â± 0.2) = _________________________________

(6 points)

On the energy level diagram below illustrate a process that involves absorption, nonradiative relaxation, and fluorescence. Use arrow notation and label each transition.

________________ v = 4

________________ v = 3

________________ v = 2

________________ v = 1

E1 ________________ v = 0

________________ v = 4

________________ v = 3

________________ v = 2

________________ v = 1

E0 ________________ v = 0

https://brainmass.com/chemistry/modern-quantum-theory/uncertainty-significant-figures-energy-diagrams-247949

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

ind the absolute uncertainty of the following calculations and express the answer with the proper number of significant figures.

a) 2.0394 (Â± 0.0008) + 3.256 (Â± 0.004) - 1.17 (Â± 0.01) =

______________________________

When you are adding or subtracting uncertainty, you just add the values. First add the actual numbers:

2.0394 + 3.256 - 1.17 = 4.1254 ïƒ 4.13 (the third number only has hundredths place)

Now add the uncertainties:

0.0008 + 0.004 + 0.01 = 0.0148. This needs to be 0.01 because it is the smallest place of the number ...

#### Solution Summary

This solution explains:

1) How to find absolute uncertainty and how to use significant figures in mathematical calculations.

2) How an energy level diagram representing absorption, nonradiative relaxation, and fluorescence will appear.