SATHEE: Structure of Atom - Result Question 30

Structure of Atom - Result Question 30

####32. Uncertainty in position of an electron $(.$ mass $. = 9.1 \times 10^{- 28} g)$ moving with a velocity of $3 \times 10^{4} c m / s$ accurate upto $0.001$ will be (use $h / 4 (π)$ in uncertainty expression where $h = 6.626 \times 10^{- 27}$ erg-second)

[1995]

(a) $1.93 c m$

(b) $3.84 c m$

(d) $7.68 c m$

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Solution:

(a) Given mass of an electron $(m) = 9.1 \times 10^{- 28} g$ ; Velocity of electron $(v) = 3 \times 10^{4} c m / s$ ;

Accuracy in velocity $= 0.001$ ;

Actual velocity of the electron

$(Δ v) = 3 \times 10^{4} \times \frac{0.001}{100} = 0.3 c m / s$ .

Planck’s constant $(h) = 6.626 \times 10^{- 27}$ erg-sec. $∴$ Uncertainty in the position of the electron

$(Δ x) = \frac{h}{4 π m Δ v} = \frac{6.626 \times 10^{- 27} \times 7}{\begin{matrix} 4 \times 22 \times (9.1 \times 10^{- 28}) \times 0.3 \\ = 1.93 c m \end{matrix}}$

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Structure of Atom - Result Question 30

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