(A) Given mass $m = 10 \, g = 0.01 \, kg$. Velocity $v = 90 \, ms^{-1}$. Uncertainty in velocity $\Delta v = 5 \, \% \text{ of } 90 = 90 \times 0.05 =

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(A) Given mass $m = 10 \, g = 0.01 \, kg$. Velocity $v = 90 \, ms^{-1}$. Uncertainty in velocity $\Delta v = 5 \, \% \text{ of } 90 = 90 \times 0.05 = 4.5 \, ms^{-1}$. According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta v \ge \frac{h}{4 \pi m}$. Substituting the values: $\Delta x = \frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 0.01 \times 4.5}$. $\Delta x = \frac{6.63 \times 10^{-34}}{0.5652} \approx 1.17 \times 10^{-33} \, m$. Rounding to the nearest integer,we get $1 \times 10^{-33} \, m$.

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

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$A$ ball weighing $10 \, g$ is moving with a velocity of $90 \, ms^{-1}$. If the uncertainty in its velocity is $5 \, \%$,then the uncertainty in its position is ....... $\times 10^{-33} \, m$. (Rounded off to the nearest integer) [Given : $h = 6.63 \times 10^{-34} \, Js$]

A
$1$
B
$2$
C
$3$
D
$10$

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Structure of Atom

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Uncertainty principle and Schrodinger wave equation

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DifficultAP EAMCET 2006

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DifficultTS EAMCET 2024

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$A$ ball weighing $10 \, g$ is moving with a velocity of $90 \, ms^{-1}$. If the uncertainty in its velocity is $5 \, \%$,then the uncertainty in its position is ....... $\times 10^{-33} \, m$. (Rounded off to the nearest integer) [Given : $h = 6.63 \times 10^{-34} \, Js$]

Similar Questions

What is the value of $\Delta v \cdot \Delta x$ for an electron? What does it indicate?

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?

Write down the Schrodinger wave equation for the hydrogen atom.

Each quantum mechanical wave function does not have a readily interpretable physical meaning,but the square of the wave function gives the . . . . . . of finding the electron at a certain point.

The uncertainty in the determination of the position of a small ball of mass $10 \ g$ is $10^{-33} \ m$. With what percentage of accuracy can its speed be measured, if it has a speed of $52.5 \ m \ s^{-1}$? (Given: $h = 6.6 \times 10^{-34} \ J \ s$)

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