Ameasurement of an electron's speed is 2.0x10^6 m/s and has an uncertainty of 10%. what is the minimum uncertainty in its position? a) 0.10 nm b) 0.23 nmm c) 0.58 nm d) 1.0 nm e) 2.3 nm

minimum uncertainty is 2.9 nm

Explanation:

Given data

electron's speed = 2.0 x 10^6 m/s

uncertainty = 10%

to find out

minimum uncertainty

solution

first we find out here electron momentum that is mass × velocity

and we know mass is 9.10 × kilograms

so momentum p = 9.10 ×  × 2.0 x  

momentum p = 1.82 ×  kilograms m /s

and  uncertainty = 10% so

change in momentum Δp = 1.82 ×   × 10%

so Δp = 1.82 × kilograms m /s

and

minimum uncertainty Δx  will be calculated by heisenberg uncertainty principle  that is

ΔpΔx  ≥ h / 4π

so Δx =  h / 4π Δp

Δx =  6.625×  / 4(π) 1.82 ×

Δx = 2.9 × m

so  minimum uncertainty is 2.9 nm

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.