(B) According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.Given that $\Delta x = \Delta p$,we substitute this

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$\sqrt{\frac{h}{4 \pi}} \times \frac{1}{m}$

(B) According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.Given that $\Delta x = \Delta p$,we substitute this into the equation: $(\Delta p)^2 = \frac{h}{4\pi}$.Since $\Delta p = m \Delta v$,we have $(m \Delta v)^2 = \frac{h}{4\pi}$.Expanding this gives $m^2 \Delta v^2 = \frac{h}{4\pi}$.Solving for $\Delta v^2$,we get $\Delta v^2 = \frac{h}{4\pi m^2}$.Taking the square root of both sides,we obtain $\Delta v = \frac{1}{m} \sqrt{\frac{h}{4\pi}}$.

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

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If uncertainties in the measurement of position and momentum of a microscopic object of mass $m$ are equal,then the uncertainty in the measurement of velocity is given by the expression:

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A
$\sqrt{\frac{h}{4 \pi m}}$
B
$\sqrt{\frac{h}{4 \pi}} \times \frac{1}{m}$
C
$\frac{h}{4 \pi} \times \sqrt{\frac{1}{m}}$
D
$\sqrt{\frac{h}{2 \pi m}}$

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Structure of Atom

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Uncertainty principle and Schrodinger wave equation

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When the uncertainty in the position of a moving particle is $0$,then the uncertainty in momentum $(p)$ is equal to:

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Which of the following statements is incorrect?

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If the position of the electron was measured with an accuracy of $\pm 0.002 \ nm$,the uncertainty in the momentum of it would be (in $kg \ ms^{-1}$) $(h=6.626 \times 10^{-34} \ J \ s)$.

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If the uncertainty in velocity and position of a minute particle in space are $2.4 \times 10^{-26} \, m \, s^{-1}$ and $10^{-7} \, m$ respectively,the mass of the particle in $g$ is $....$ (Nearest integer).
(Given: $h = 6.626 \times 10^{-34} \, J \, s$)

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Assertion $(A)$: The probability of finding an electron in a small volume around a point $(x, y, z)$ at a distance $r$ from the nucleus is proportional to $\psi^2$.
Reason $(R)$: Subatomic particles possess both particle and wave nature.

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If uncertainties in the measurement of position and momentum of a microscopic object of mass $m$ are equal,then the uncertainty in the measurement of velocity is given by the expression:

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When the uncertainty in the position of a moving particle is $0$,then the uncertainty in momentum $(p)$ is equal to:

Which of the following statements is incorrect?

If the position of the electron was measured with an accuracy of $\pm 0.002 \ nm$,the uncertainty in the momentum of it would be (in $kg \ ms^{-1}$) $(h=6.626 \times 10^{-34} \ J \ s)$.

If the uncertainty in velocity and position of a minute particle in space are $2.4 \times 10^{-26} \, m \, s^{-1}$ and $10^{-7} \, m$ respectively,the mass of the particle in $g$ is $....$ (Nearest integer).(Given: $h = 6.626 \times 10^{-34} \, J \, s$)

Assertion $(A)$: The probability of finding an electron in a small volume around a point $(x, y, z)$ at a distance $r$ from the nucleus is proportional to $\psi^2$.Reason $(R)$: Subatomic particles possess both particle and wave nature.

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If the uncertainty in velocity and position of a minute particle in space are $2.4 \times 10^{-26} \, m \, s^{-1}$ and $10^{-7} \, m$ respectively,the mass of the particle in $g$ is $....$ (Nearest integer).
(Given: $h = 6.626 \times 10^{-34} \, J \, s$)

Assertion $(A)$: The probability of finding an electron in a small volume around a point $(x, y, z)$ at a distance $r$ from the nucleus is proportional to $\psi^2$.
Reason $(R)$: Subatomic particles possess both particle and wave nature.