In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000\pm40 nuclei decayed in the first 1.0s. For |x| ≪ 1,\text{\ln}(1+x)x up to first power in x. The error \Delta\lambda,in the determination of the decay constant \lambda in S^{-1},is [JEE Adv 2018 P1]

Units and Measurements

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If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. Forexample, consider the relation z=

. If the errors in x,y and z are Δx,Δy and Δz ,respectively, then

z±Δz=

x±Δx

y±Δy

(1±

Δx

)(1±

Δy

)−1

The series expansion for (1±

Δy

)−1 ,to first power in Δy/y , is 1∓(Δy/y) .The relative errors in independent variables are always added. So the error in z will be Δz=(

Δx

Δy

)
The above derivation makes the assumption that Δx/x<<1,Δy/y<<1 .
Therefore, the higher power of these quantities are neglected.

Section: Physics

Question : 17 of 34

Marks: +1, -0

In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000±40 nuclei decayed in the first 1.0s.
For |x|≪1,ln(1+x)x up to first power in x.
The error Δλ,in the determination of the decay constant λ in S−1,is

[JEE Adv 2018 P1]

0.04
0.03
0.02
0.01

Validate

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