Chemistry, 24.06.2021 01:00 Kadyn5

Perform the calculations and determine the absolute and percent relative uncertainty. Express each answer with the correct number of significant figures. a. [9.8(±0.3)−2.31(±0.01)]8.5(±0.6)=
b. absolute uncertainty:
c. absolute uncertainty:
d. percent relative uncertainty:

Answers: 2

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Answer from: DenniJ19

Explanation:

Given the equation:

$\implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}$

The absolute uncertainty in a measurement is the term used to describe the degree of inaccuracy.

The first step is to determine the algebraic value on the numerator.

Algebraic value = 9.8 - 231

= 7.49

The absolute uncertainty = $\sqrt{(abs. uncertainty_{v_1})^2+(abs. uncertainty_{v_2})^2}$

absolute uncertainty = $\sqrt{(0.3)^3 + (0.01)^2}$

= $\sqrt{0.09 + 0.0001}$

= 0.300167

∴

[9.8(±0.3) - 2.31(±0.01)] = 7.49(±0.300167)

The division process now is:

$\implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}= \dfrac{7.49 (\pm 0.300167)}{8.5 (\pm0.6)}$

Relative uncertainty = $\dfrac{(\pm 0.300167)}{7.49}\times 100 \ , \ \dfrac{(\pm 0.6) }{8.5} \times 100$

Relative uncertainty = ±4.007565% , ±7.058824%

$\text{Relative uncertainty} = \sqrt{(4.007565)^2+(7.058824)^2}$

$\text{Relative uncertainty} = \sqrt{16.06057723+49.82699626}$

$\text{Relative uncertainty} = \sqrt{65.88757349}$

$\text{Relative uncertainty} = 8.117116$

≅ 8%

The algebraic value = $\dfrac{7.49}{8.5}$

= 0.881176

≅ 0.88

The percentage of the relative uncertainty = $\dfrac{\text{Absolute uncertainty }}{\text{calculated value} }\times 100$

By cross multiplying:

$\text{Absolute uncertainty} (\%) = \dfrac{\text{relative uncertainty} \times \text{calculated value}}{100}$

$\text{Absolute uncertainty} (\%) = \dfrac{8.117116\times 0.881176}{100}$

$\text{Absolute uncertainty} (\%) = 0.0715260$

$\mathbf{\text{Absolute uncertainty} (\%) \simeq 0.07}$

Finally:

$\mathbf{\implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}= 0.88 \pm (0.07) \pm 8\%}$

Answer from: Quest

The answer is c) pyrite

Answer from: Quest

remember that hf is only the energy of one photon. not two. not three. one. 1) 5.12 * 10^3 photons find the energy of one photon, then determine how many photons are needed to reach the sensitivity. e = hf = (6.626 * 10^-34 js)(5.95 * 10^19 hz) = 3.94247 * 10^-14 j per photon (2.02 * 10^-10 j) / (3.94247 * 10^-14 j/photon) = 5123.69149 photons round to three sig figs. 2) 5.77 * 10^-17 j energy of pulse = energy per photon * number of photons = hfn = (6.626 * 10^-34 js)(1.66 * 10^13 hz)(5250) = 5.774559 * 10^-17 j round to three sig figs. 3) 4.07 * 10^8 kj/mol 10^12 pm = 1 m c = fλ f = c/λ e = hf = hc/λ = [(6.626 * 10^-34 js)(3.00 * 10^8 m/s) / (2.94 * 10^-12 m)](1 kj/1000 j)(6.02 * 10^23 photons/mol) = 40702571.4 kj/mol round to three sig figs. 4) 9.94 * 10^-1 m e = hc/λ λ = hc / e = (6.626 * 10^-34 js)(3.00 * 10^8 m/s) / (2.00 * 10^-25 j) = 0.9939 m round to three sig figs. 5) 9.06 * 10^3 photons energy of pulse = energy per photon * number of photons number of photons = energy of pulse / energy per photon = energy of pulse / (hf) = (3.87 * 10^-13 j) / [(6.626 * 10^-34 js)(6.45 * 10^16 hz)] = 9055.23695 photons round to three sig figs. 6) 2.78 * 10^-15 j this is problem 1, except in reverse. sensitivity = minumum number of photons * energy per photon = (5930)(6.626 * 10^-34 js)(7.077 * 10^14 hz) = 2.78070758 × 10^-15 j round to three sig figs.

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