S C Kheterpal, S N Dhawan and, P N Kapil Solutions for Chapter: Structure of Atom, Exercise 7: PROBLEMS FOR PRACTICE

The uncertainty in position and velocity of a particle are: ${10}^{-10}\mathrm{m}$ and $5.27\times {10}^{-27} \mathrm{m} {\sec }^{-1}$ respectively. Calculate the mass of the particle $\left(\mathrm{h}=6.625\times {10}^{-34}\mathrm{J}\mathrm{}\mathrm{s}\mathrm{e}\mathrm{c}\right).$

The mass of an electron is $9.11\times {10}^{-31}\mathrm{k}\mathrm{g}.$ Calculate the uncertainty in its velocity if the uncertainty in its position is of the order of $\pm 10 \mathrm{p}\mathrm{m} \left(\mathrm{h}=6.6\times {10}^{-34} \mathrm{k}\mathrm{g} {\mathrm{m}}^2 {\mathrm{s}}^{-1}\right).$

An electron has a speed of $500 \mathrm{m}{\mathrm{s}}^{-1}$ with an uncertainty of $0.02\mathrm{\%}.$ What is the uncertainty in locating its position? $\left[\mathrm{G}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n} \mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}=9.1\times {10}^{-31} \mathrm{k}\mathrm{g}, \mathrm{h}=6.6\times {10}^{-34} \mathrm{J}\mathrm{s}\right]$

A proton is accelerated to a velocity of $3\times {10}^7 \mathrm{m}{\mathrm{s}}^{-1}.$ If the velocity can be measured with a precision of $\pm 0.5\mathrm{\%},$ calculate the uncertainty in position of proton $\left[\mathrm{h}=6.6\times {10}^{-34}\mathrm{J}\mathrm{s}, \mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s} \mathrm{of} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}=1.66\times {10}^{-27} \mathrm{k}\mathrm{g}\right].$

Calculate the uncertainty in the position of a dust particle with mass equal to $1\mathrm{}\mathrm{m}\mathrm{g}$ if the uncertainty in its velocity is $5.5\times {10}^{-20}{\mathrm{m}\mathrm{s}}^{-1}.$

The uncertainty in the momentum of a particle is $2.2\times {10}^{-4} \mathrm{g} \mathrm{c}\mathrm{m} {\mathrm{s}}^{-1}.$ With what accuracy can its position be determined? $\left(\mathrm{h}=6.626\times {10}^{-27}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{}\mathrm{s}\right)$

Calculate the uncertainty in the velocity of an electron if the uncertainty in its position is $1\mathrm{Å}$ or $100\mathrm{}\mathrm{p}\mathrm{m}\left({10}^{-10}\mathrm{m}\right).$

What is the minimum uncertainty in the position of a bullet of mass $5\mathrm{g}$ that is known to have a speed somewhere between $\mathrm{550,00000}$ and $\mathrm{550,00001}\mathrm{}{\mathrm{m}\mathrm{s}}^{-1}?$