Heisenberg's Uncertainty Principle

Q.

The uncertainty in momentum of an electron is $1\times {10}^{-5}kg-m/s$. The uncertainty in its position will be ($h=6.62\times {10}^{-34}kg-m^2/s$)

1. 1.05×10^-28 m

2. 1.05×10^-26 m

3. 5.25×10^-28 m

4. 5.27×10^-30 m

Q. The orbital angular momentum for an electron revolving in an orbit is given by $\sqrt{1(1+1)}\frac{h}{2\pi }$. What is the orbital angular momentum of an s-electron?

1. 1

2. 2

3. 0

4. 6

Q.

According to Heisenberg's uncertainty principle, the product of uncertainties in position and velocities for an electron of mass 9.1 $\times$ ${10}^{-31}$ kg is

1. 2.8 × 10^-3 m² s^-1

2. 3.8 × 10^-5 m² s^-1

3. 5.8 × 10^-5 m² s^-1

4. 6.8 × 10^-6 m² s^-1

Q.

Calculate the uncertainty in the velocity of a wagon of mass, $3000\mathrm{Kg}$ whose position is known to an accuracy of $10\mathrm{pm}.$

Q.

Assuming that the Pauli exclusion principle is non-existent, which of the following will be the most unacceptable configuration of Li in the ground state?

1. 1 2

2. 1

3. 1 2

4. 1 2 2

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.

If uncertainty in the position of an electron is zero, the uncertainty in its momentum would be

1. Zero

2. 

3. 

4. Infinite

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

Q. If uncertainty in position and momentum are equal, then uncertainty in velocity is eqaul to:

1. $\frac{1}{m}\times \sqrt{\frac{h}{\pi }}$
2. $\frac{h}{\pi }$
3. $\frac{1}{2m}\times \sqrt{\frac{h}{\pi }}$
4. $\sqrt{\frac{h}{2\pi }}$

Q.

A green ball weighs 80 g and comes travelling towards you at 900 m/s. A photon of light emitted from green ball has a wavelength of $6\times {10}^{-7}$ m. Assuming that the error in the position of ball is the same as the wavelength of its photon, calculate error in the momentum (kgm/s) of the green ball.

1. $1.054\times {10}^{-30}$
2. $1.054\times {10}^{-23}$
3. $2.786\times {10}^{-23}$
4. $8.75\times {10}^{-29}$

Q.

A golf ball has a mass of 40g and a speed of 45 m$s^{-1}$. If the speed can be measured with an accuracy of 2%, calculate the uncertainty in the position.

1. 1.46 $\times$ ${10}^{-33}$ m

2. 2.62 $\times$ ${10}^{-34}$ m

3. 7.84 $\times$ ${10}^{-35}$ m

4. 5.55 $\times$ ${10}^{-33}$ m

Q. If the position of the electron is measured within an accuracy of $\pm$0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is $\frac{h}{4\pi m}\times 0.05nm$, is there any problem in defining this value?

Q. What shall be the minimum percentage error in velocity if the uncertainty in position is equal to the de Broglie wavelength of a particle?

1. $\frac{h}{4\pi }$
2. $25\pi$
3. $\frac{100}{\pi }$
4. $\frac{25}{\pi }$

Q.

According to Heisenberg's uncertainty principle, the product of uncertainties in position and velocities for an electron of mass 9.1 $\times$ ${10}^{-31}$ kg is

1. 2.8 $\times$ ${10}^{-3}$ $m^2$ $s^{-1}$

2. 3.8 $\times$ ${10}^{-5}$ $m^2$ $s^{-1}$

3. 5.8 $\times$ ${10}^{-5}$ $m^2$ $s^{-1}$

4. 6.8 $\times$ ${10}^{-6}$ $m^2$ $s^{-1}$

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

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

Q. The measurement of the position of the electron is associated with an uncertainty in momentum, which is equal to $2.5\times {10}^{-8}{\text{g cm s}}^{-1}$. The uncertainty in the velocity of the electron is:

(Mass of an electron is $9\times {10}^{-28}\text{g})$

1. $1\times {10}^9{\text{cm s}}^{-1}$
2. $2.725\times {10}^9{\text{cm s}}^{-1}$
3. $27.25\times {10}^9{\text{cm s}}^{-1}$
4. $2.275\times {10}^9{\text{cm s}}^{-1}$

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

Q. Given : The mass of electron is $9.11\times {10}^{–31}kg$, Planck constant is $6.626\times {10}^{–34}Js$, the uncertainty involved in the measurement of velocity within a distance of $0.1\AA$ is:

1. $5.79\times {10}^{5}m{s}^{-1}$
2. $5.79\times {10}^{6}m{s}^{-1}$
3. $5.79\times {10}^{7}m{s}^{-1}$
4. $5.79\times {10}^{8}m{s}^{-1}$

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

Q.

In an atom, an electron is moving with a speed of $600m/s$ with an accuracy of 0.005 %. Certainity with which the position of the electron can be located is

($h=6.6\times {10}^{-34}kg{m}^2{s}^{-1}$, 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. $1.52\times {10}^{-4}m$

Q. Compared to the uncertainty associated with 1kg iron ball, the uncertainty of electron is:
(Assume both are moving in the same speed)

1. 10 times
2. ${10}^2$ times
3. ${10}^{23}$ times
4. ${10}^{30}$ times

Q.

According to bohrs atomic model the value of which among the following quantity is quantized for an electron?

1. its angular velocity
2. its angular momentum
3. its linear velocity
4. its linear momentum

Q. Calculate the velocity of moving electron in the third orbit of bohrs atomic model of hydrogen. Also calculate the number of revolution per second that the electron make around the nucleus.

Q. according to bohr model of hydrogen atom
a.) Total energy of the electron is quantized
b.) angular momentum of the electron is quantized and given as ?{l(l+1)}*h/2?
C.) both A and B
d.) none of these

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.

Calculate the uncertainty in the position ($\Delta x)$ of an electron if $\Delta vis0.1\%$. Take the velocity of electron $=2.2\times {10}^{6}m{s}^{-1}$ and mass of electron as $9.108\times {10}^{-31}kg$.

1. $262.48\times {10}^{-10}m$

2. $9.1\times {10}^{-9}m$

3. $458.76\times {10}^{-12}m$

4. $959.67\times {10}^{-10}m$

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