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

May 10, 2018

See below:

#### Explanation:

For (i):

From my measurement by eye, it seems that the point where $\lambda = 5.0 \times {10}^{5}$, $y = 0.35 c m$. The bars stretch up until 0.4 cm so the fractional uncertainty on the measurement should be approximately $\pm 0.05 c m$

So the fractional uncertainity is:

$\frac{0.05}{0.35} \approx 0.14$ (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

$y = \frac{a b}{c}$

Then the uncertainties are:

$\frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}$

hence:

$\frac{\Delta y}{0.35} ^ 2 = \left(\frac{0.05}{0.35}\right) + \left(\frac{0.05}{0.35}\right)$

$\frac{\Delta y}{0.35} ^ 2 = \frac{0.1}{0.35}$

$\frac{\Delta y}{0.35} ^ 2 \approx 0.28$ so the percentage uncertainty is 28% or the fractional uncertainty is 0.28.