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Heisenberg’s uncertainty principle - (Concept)
Heisenberg’s uncertainty principle:
It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.
If an attempt is made to ensure that any one of these two quantities are measured with a higher accuracy, then the other quantity becomes less accurate.
Mathematically, the product of uncertainty in position(Δx) and uncertainty in momentum(ΔP) is equal to or greater than h/4π
$\Delta x . \Delta P \geq \frac{h}{4 \pi}$
It can be proved mathematically that the uncertainty principle is only significant to subatomic particles but not insignificant for everyday large sized objects.
| Exam | Chapter |
| JEE MAIN | Atomic Structure |
A ball weighing 10g is moving with velocity of 90ms-1. If the uncertainty in its velocity is 5%, the uncertainty in its position is _______. (Rounded off to the nearest integer)
[Given : ]
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The uncertainty in momentum of an electron is . The uncertainty in its position will be
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If the uncertainty in velocity and position of a minute particle in space are, respectively. The mass of the particle in
is____________.(Nearest integer)
(Given : )
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The minimum uncertainty in the speed of an electron in a one-dimensional region of length
is _____________
.
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An accelerated electron has a speed of $5 \times 10^6 \mathrm{~ms}^{-1}$ with an uncertainty of $0.02 \%$. The uncertainty in finding its location while in motion is $x \times 10^{-9} \mathrm{~m}$. The value of $x$ is $\qquad$ .(Nearest integer)
[Use mass of electron
$$
\left.=9.1 \times 10^{-31} \mathrm{~kg}, h=6.63 \times 10^{-34} \mathrm{Js}, \pi=3.14\right]
$$
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Uncertainty in the position of an electron moving with a velocity
, accurate upto 0.001% is approximately
. The value of
is
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In an atom, an electron is moving with a speed of 600 m/s with an uncertainty of 0.005%. Uncertainty with which the position of the electron can be located is X m. The value of X is
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Uncertainty in position of a minute particle of mass 25 g in space is $10^{-5} \mathrm{~m}$. What is the uncertainty in its velocity $\left(\right.$ in $\left.\mathrm{ms}^{-1}\right)$ ?
$
\left(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}\right)
$
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Given below are two statements:
Statement I : According to Bohr's model of hydrogen atom, the angular momentum of an electron in a given stationary state is quantised.
Statement II: The concept of an electron in Bohr's orbit. violates the Heisenberg uncertainty principle. In the light of the above statements, choose the most appropriate answer from the options given below.
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Uncertainty in position of a minute particle of mass 25 g in space is What is the uncertainty in its velocity
?
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Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter $10^{-15} \mathrm{~m}$ is __________ $\times 10^9 \mathrm{~ms}^{-1}$ (nearest integer)
[Given : mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$, Planck's constant $(\mathrm{h})=6.626 \times 10^{-34} \mathrm{Js}$ ]
(Value of $\pi=3.14$ )
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The uncertainty in the position of an electron moving with a velocity of $3 \times 10^4 \mathrm{~cm} / \mathrm{sec}$ accurate up to $0.011 \%$ will be
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Given below are two statements :
Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.
Statement (II) : If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is $\geq \sqrt{\frac{\mathrm{h}}{\pi}} \times \frac{1}{2 \mathrm{~m}}$.
In the light of the above statements, choose the correct answer from the options given below :
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Which of the following is responsible to rule out the existence of definite paths or trajectories of electrons?
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It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.
