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Uncertainty principle and Schrodinger wave equation Questions in English

Class 11 Chemistry · Structure of Atom · Uncertainty principle and Schrodinger wave equation

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151
EasyMCQ
Which one of the following conditions is incorrect for a well-behaved wave function $(\psi)$?
A
$\psi$ must be finite
B
$\psi$ must be single-valued
C
$\psi$ must be infinite
D
$\psi$ must be continuous

Solution

(C) For a well-behaved wave function,the $BORN$ conditions are that $\psi$ must be finite,single-valued,and continuous. Therefore,the condition that $\psi$ must be infinite is incorrect.
152
MediumMCQ
Which of the following does not represent the mathematical expression for the $\text{HEISENBERG}$ uncertainty principle?
A
$\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}$
B
$\Delta x \cdot \Delta v \geq \frac{h}{4 \pi m}$
C
$\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}$
D
$\Delta E \cdot \Delta x \geq \frac{h}{4 \pi}$

Solution

(D) According to the $\text{HEISENBERG}$ uncertainty principle,the product of uncertainty in position and momentum is given by $\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}$.
Since $\Delta p = m \Delta v$,substituting this into the equation gives $\Delta x \cdot m \Delta v \geq \frac{h}{4 \pi}$,which simplifies to $\Delta x \cdot \Delta v \geq \frac{h}{4 \pi m}$.
Additionally,the principle can be expressed in terms of energy and time as $\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}$.
Therefore,the expression $\Delta E \cdot \Delta x \geq \frac{h}{4 \pi}$ is incorrect.

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