An α$$-particle$$ moving with velocity $$130th$$ times velocity of light. If uncertainty in position is $$3.31$$$$π$$pm, then minimum uncertainty in kinetic energy y × $$10-16$$ J. Calculate the value of y.

$$dKE=mv$$ dv $$=$$ mv $$h4$$$$π$$m∆$$x=3$$×$$10830$$×$$6.62$$×$$10-344$$×π×$$3.31$$π×$$10-12=5$$×$$10-16J$$

Quantum mechanical model of the atom

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Question

An $α$ -particle moving with velocity $\frac{1}{30}$ th times velocity of light. If uncertainty in position is $\frac{3.31}{π}$ pm, then minimum uncertainty in kinetic energy y × 10^-16 J. Calculate the value of y.

Moderate

Solution

$d (KE) = mv dv = mv \frac{h}{4 πm ∆ x}$
$= \frac{3 \times 10^{8}}{30} \times \frac{6.62 \times 10^{- 34}}{4 \times π \times \frac{3.31}{π} \times 10^{- 12}}$
=5×10^-16J

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