(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:

AP EAMCET 2018 All AP EAMCET

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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Uncertainty principle and Schrodinger wave equation

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The uncertainties in the velocities of two particles,$A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times that of the mass of $A$. What is the ratio of uncertainties $\frac{\Delta x_A}{\Delta x_B}$ in their positions?

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Which of the following quantum numbers is not obtained by the solution of the Schrodinger wave equation?

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For a particle of mass $0.02 \, kg$,the uncertainty in its velocity is $9.218 \times 10^{-6} \, m/s$. The uncertainty in its position is .......

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In an atom,an electron is moving with a speed of $600 \, m/s$ with an accuracy of $0.005 \%$. The certainty with which the position of the electron can be located is $(h = 6.6 \times 10^{-34} \, kg \, m^2 s^{-1}, m_e = 9.1 \times 10^{-31} \, kg)$:

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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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Choose the correct statement.

The uncertainties in the velocities of two particles,$A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times that of the mass of $A$. What is the ratio of uncertainties $\frac{\Delta x_A}{\Delta x_B}$ in their positions?

Which of the following quantum numbers is not obtained by the solution of the Schrodinger wave equation?

For a particle of mass $0.02 \, kg$,the uncertainty in its velocity is $9.218 \times 10^{-6} \, m/s$. The uncertainty in its position is .......

In an atom,an electron is moving with a speed of $600 \, m/s$ with an accuracy of $0.005 \%$. The certainty with which the position of the electron can be located is $(h = 6.6 \times 10^{-34} \, kg \, m^2 s^{-1}, m_e = 9.1 \times 10^{-31} \, kg)$:

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