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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3as154

Use $h = 6.626 \times 1 0^{- 34} J s$ and $m_{e} = 9.1 \times 1 0^{- 31} kg$ with $Δ x Δ p = h /4 π$ . Select the correct statements.

AFor an electron with $Δ x = 1 \overset{˚}{A}$ , the minimum $Δ v$ is about $5.8 \times 1 0^{5} m s^{- 1}$ .
BFor a $1 g$ particle with $Δ x = 1 \overset{˚}{A}$ , the minimum $Δ v$ is about $5.3 \times 1 0^{- 22} m s^{- 1}$ .
CThe minimum value of $Δ x Δ p$ is about $5.3 \times 1 0^{- 35} J s$ .
DFor the electron in option A, $Δ v$ is larger than for the $1 g$ particle of option B by a factor of $1 0^{3}$ .

Answer: A, B, C

Δ v = h / (4 πm Δ x)

: electron gives

5.79 \times 1 0^{5} m/s

(A true); 1 g gives

5.27 \times 1 0^{- 22} m/s

(B true).

h /4 π = 5.27 \times 1 0^{- 35} J s

(C true). The ratio of the two velocity uncertainties is

m_{1 g} / m_{e} = 1.1 \times 1 0^{27}

, not

1 0^{3}

(D false).

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