SATHEE: Structure of Atom - Result Question 26

Structure of Atom - Result Question 26

####28. If uncertainty in position and momentum are equal, then uncertainty in velocity is : [2008]

(a) $\frac{1}{2 m} \sqrt{\frac{h}{π}}$

(b) $\sqrt{\frac{h}{2 π}}$

(c) $\frac{1}{m} \sqrt{\frac{h}{π}}$

(d) $\sqrt{\frac{h}{π}}$

Show Answer

Solution:

(a) We know $Δ p \cdot Δ x \geq \frac{h}{4 π}$

or $m \cdot Δ v \cdot Δ x = \frac{h}{4 π} [∴ Δ p = m Δ v]$

since $Δ p = Δ x$ (given)

$∴ Δ p \cdot Δ p = \frac{h}{4 π}$ or $m Δ v m Δ v = \frac{h}{4 π}$

or $(Δ v)^{2} = \frac{h}{4 π m^{2}}$

or $Δ v = \sqrt{\frac{h}{4 π m^{2}}} = \frac{1}{2 m} \sqrt{\frac{h}{π}}$

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