Heisenberg's Uncertainty Principle

Q. In an atom, an electron is moving with the speed of 600 $m/s$ have an accuracy of 0.005%. The minimum uncertainity with which the position of the electron can be located is:
$h=6.6\times {10}^{-34}Js,\text{mass of electron},e_m=9.1\times {10}^{-31}kg$

1. $5.10\times {10}^{-3}m$
2. $1.92\times {10}^{-3}m$
3. $3.84\times {10}^{-3}m$
4. $1.52\times {10}^{-3}m$

Q. An atom typically exists in an excited state for about $\Delta t={10}^{-8}$ s. Estimate the uncertainity in frequency $\Delta \nu$ in the frequency of emitted photons when an atom makes a transition from an excited state with the simultaneous emission of a photon with an average frequency of ${\nu }_{av}$ = $7.1\times {10}^{14}$ Hz. Calculate the ratio of uncertainity in frequency to the average frequency.

1. $1.12\times {10}^{-10}$
2. $2.11\times {10}^{-8}$
3. $2.11\times {10}^{-10}$
4. $1.12\times {10}^{-8}$

Q.

An electron has a speed of 500 m/s with an uncertainty of 0.02% What is the uncertainty in position?

Q. distinguish between orbit and orbital

Q. The frequency of radiation emitted when the electron falls from n = 4 to n = 1 in a hydrogen atom will be (given ionization energy of $H=2.18\times {10}^{-18}ato{m}^{-1}$ and $h=6.606\times {10}^{-34}j-s$)

1. 1.54 X 10¹⁵ s^-1
2. 1.03 X 10¹⁵ s^-1
3. 3.08 X 10¹⁵ s^-1
4. 2 X 10¹⁵ s^-1

Q. The uncertainty in the position of an electron ( mass $=9.1\times {10}^{-28}g$) moving with a velocity of $3.0\times {10}^{4}cm{s}^{-1}$ accurate upto 0.001% will be

1. 1.92 cm
2. 7.68 cm
3. 5.76 cm
4. 3.84 cm

Q. The minimum uncertainty in the speed of an electron in a one dimensional region of length \(2a_0\) (where \(a_0=\)Bohar radius \(52.9\) pm) is \(km~s^{-1}\).

(Given : Mass of electron \(=9.1\times 10^{-31}\) kg, Plancks constant \(h=6.63\times 10^{-34}Js\))

Q. The angular momentum of an electron in 2s orbital is:

1. zero
2. 
3. 
4. 

Q.

For the $1s$ orbital of the Hydrogen atom, the radial wave function is given as:
$R\left(r\right)=\frac{1}{\sqrt{\pi }}{\left(\frac{1}{a_0}\right)}^{\frac{3}{2}}{e}^{\frac{-r}{a_0}}$ (Where $a_0=0.529\stackrel{\circ }{A}$)

The ratio of radial probability density of finding an electron at $r=a_0$ to the radial probability density of finding an electron at the nucleus is given as $(x.e^{-y})$.
Calculate the value of $(x+y)$.

Q. The difference between orbital angular momentum of an electron in a $4f$ orbital and another electron in a $4s$ orbital is:

1. $2\sqrt{3}$
2. $3\sqrt{2}$
3. $\sqrt{3}$
4. $2$

Q. Calculate the uncertainity in velocity of a cricket ball of mass 150 g if the uncertainty in its position is of the order of $1\stackrel{o}{A}.$
$(h=6.6\times {10}^{-34}kg{m}^2{s}^{-1})$

1. $5.809\times {10}^{-24}m{s}^{-1}$
2. $3.5\times {10}^{-24}m{s}^{-1}$
3. $9.077\times {10}^{-24}m{s}^{-1}$
4. $1.908\times {10}^{-24}m{s}^{-1}$

Q. Alveoli are tiny sacs in the lungs whose average diameter is $5\times {10}^{-10}m$. Consider an oxygen molecule $(5.3\times {10}^{-26}kg)$ trapped within an alveolus. Calculate the uncertainty in the velocity of the oxygen molecule.

1. $2.05m{s}^{-1}$
2. $1.50m{s}^{-1}$
3. $1.20m{s}^{-1}$
4. $0.20m{s}^{-1}$

Q. The uncertainty in the position of an object weighing 40 g is $\pm {10}^{-3}m$. Calculate the uncertainty in its velocity.

1. $1.32\times {10}^{-30}m/s$
2. $2.63\times {10}^{-29}m/s$
3. $0.55\times {10}^{-30}m/s$
4. $4.55\times {10}^{-29}m/s$

Q.

Explain de Broglie wave theory

Q. Uncertainty in the position of an electron (mass = $9.1\times {10}^{-31}kg$) moving with a velocity of 300 m/s accurate upto 0.001% will be:

1. $5.76\times {10}^{-3}$ $m$
2. $1.92\times {10}^{-2}$ $m$
3. $3.84\times {10}^{-3}$ $m$
4. $19.2\times {10}^{-4}$ $m$

Q. The lifetime of an excited state of an atom is $3\times {10}^3$ s. What will be the minimum uncertainity in the Energy?

1. $1.76\times {10}^{-35}$ J
2. $1.76\times {10}^{-34}$ J
3. $1.76\times {10}^{-33}$ J
4. $1.76\times {10}^{-38}$ J

Q. In Heisenberg's uncertainty principle
The expression:∆x×∆p(>or=)h/4π or h/2π
Which is correct?

Q.

Question 10

Which of the following is responsible to rule out the existence of definite paths or trajectories of electrons ?

(a) Pauli's exclusion principle

(b) Heisenberg's uncertainty principle

(c) Hund's rule of maximum multiplicity

(d) Aufbau principle

Q.

If the position of the electron is measured within an accuracy of + 0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is h/4πm × 0.05 nm, is there any problem in defining this value.

Q.

In a given atom no two electrons can have the same values for all the four quantum numbers. This is called

1. Pauli's exclusion principle

2. Uncertainty principle

3. Hund's rule

4. Aufbau's principle

Q. An atom in an excited state temporarily stores energy. If the lifetime of this excited state is measured to be $1.0\times {10}^{-10}s$ then the minimum uncertainty in the energy of the state is $X\times {10}^{-6}$ eV. Then X is . Take $h=6.6\times {10}^{-34}Jsand\pi =3$.

Q. The mass of a particle is ${10}^{-10}$ g and its radius is $2\times {10}^{-4}cm$.If its velocity is ${10}^{-6}cm{s}^{-1}$ with 0.0001% uncertainity in measurement, the uncertainity in its position is:

1. $5.2\times {10}^{-7}m$
2. $5.2\times {10}^{-6}m$
3. $5.2\times {10}^{-9}m$
4. $5.2\times {10}^{-8}m$

Q.

How to determine the exact position and momentum of an electron?

Q. In an atom, an electron is moving with a speed of 250 m/s which is measured with an accuracy of 0.001 %. Certainty with which the position of the electron can be located is:
$(h=6.6\times {10}^{-34}kg{m}^2{s}^{-1},\text{Mass of electron}=9.1\times {10}^{-31}kg)$

1. $2.30\times {10}^{-3}m$
2. $1.52\times {10}^{-4}m$
3. $5.1\times {10}^{-3}m$
4. $3.84\times {10}^{-3}m$

Q. Bohr's idea of electrons moving around the nuclei in well defined paths is not valid due to which of the following phenomena?

1. Zeeman effect
2. Stark effect
3. Heisenberg's Uncertainity Principle
4. Line spectrum of hydrogen atom

Q. An electron is allowed to move freely in a closed cubic box of length of side 10 $mm$. The uncertainity in its velocity will be:

1. $3.35\times {10}^{-3}{ms}^{-1}$
2. $5.8\times {10}^{-4}{ms}^{-1}$
3. $4\times {10}^{-5}{ms}^{-1}$
4. $4\times {10}^{-6}{ms}^{-1}$

Q.

According to Heinsbergs the principal, the product of uncertainty is position and velocity for an electron of mass -31

9.1×10

-3 -5 -5 -6

(a) 2.8×10 (b) 3.8×10 (c)5.8×10 (d)6.8×10

How to solve it

Q.

The wave mechanical model of an atom is based upon

1. de-Broglie concept of dual character of matter

2. Heisenberg’s uncertainty principle

3. Schrodinger’s wave equation

4. All the three above

Q. The mass of the particle is ${10}^{-10}$ g and its radius $2\times {10}^{-4}$ cm, if the velocity is ${10}^{-6}$ cm/s with 0.0001% uncertainty in measurement, the uncertainty in its position is:

1. 
   $5.2\times {10}^{-8}$ m
2. 
   $5.2\times {10}^{-7}$ m
3. 
   $5.2\times {10}^{-6}$ m
4. 
   $5.2\times {10}^{-9}$ m

Q.

According to the Schrodinger a particle is equivalent to:

1. a wave

2. a particle only

3. both of them

4. none of them