Question

For λ = 5.0 X 10^5m calculate the (i) fractional uncertainty in d. (ii) percentage uncertainty in d^2 ?

Answer 1

See below:

Explanation:

For (i):

From my measurement by eye, it seems that the point where `lambda=5.0 times 10^5`, `y=0.35 cm`. The bars stretch up until 0.4 cm so the fractional uncertainty on the measurement should be approximately `+- 0.05 cm`

So the fractional uncertainity is:

`0.05/(0.35) approx 0.14` (as a fractional uncertainty, 14% as a percentage uncertainty)

Uncertainties:

When two values are multiplied with uncertainties use the formula (Section 1.2 in the Physics Data booklet):

as `d^2= d times d`

If

`y=(ab)/(c)`

Then the uncertainties are:

`(Deltay)/(y)=(Deltaa)/a +(Deltab)/(b)+(Deltac)/c`

hence:

`(Deltay)/(0.35)^2=(0.05/0.35)+(0.05/0.35)`

`(Deltay)/(0.35)^2=0.1/0.35`

`(Deltay)/(0.35)^2 approx 0.28` so the percentage uncertainty is 28% or the fractional uncertainty is 0.28.