Embibe Experts Solutions for Chapter: Atomic Structure, Exercise 1: EXERCISE

Photon having energy equivalent to the binding energy of $4\mathrm{th}$ state of ${\mathrm{He}}^{+}$ atom is used to eject an electron from the metal surface of work function $1.4 \mathrm{eV}$. If the electrons are further accelerated through the potential difference of $4 \mathrm{V}$, then, the minimum value of de-Broglie wavelength in cm associated with the electron is found to be $5\times {10}^{-\mathrm{p} }\mathrm{cm}. \mathrm{Evaluate} \mathrm{p}?$

In a sample of $\mathrm{H}-$atoms, the electrons de-excite from a level ${}^{\text{'}}\mathrm{n}^{\text{'}}$ to $1$. The total number of lines belonging to the Balmer series are two. If the electrons are ionised from the level ${}^{\text{'}}\mathrm{n}^{\text{'}}$ by the photons of energy $13 \mathrm{eV}$, then determine the kinetic energy of the ejected photoelectrons.

An $\mathrm{\alpha }-$particle has an initial kinetic energy of $25 \mathrm{eV}$, and it is accelerated through the potential difference of $150$ volts. If a proton has the initial kinetic energy of $25 \mathrm{eV}$, and it is accelerated through the potential difference of $25$ volts, then find the approximate ratio of the final wavelengths associated with the proton and the $\mathrm{\alpha }-$particle.

Uncertainty in position of a particle of $25 \mathrm{g}$ in space is ${10}^{-15} \mathrm{m}$. Determine, uncertainty in velocity $\left(\mathrm{m}.{\sec }^{-1}\right)$ in it. (Plank's constant, $\mathrm{h}=6.6\times {10}^{-34} \mathrm{Js}$) If answer is $2.1\times {10}^{-\mathrm{x}}$. then x is.

The orbital angular momentum for an electron revolving in an orbit is given by $\sqrt{\mathrm{\ell }\left(\mathrm{\ell }+1\right)}\frac{\mathrm{h}}{2\mathrm{\pi }}$. Determine this momentum for an $\mathrm{s}$-electron.

Determine the wavelength of the radiation emitted, when in a hydrogen atom, the electron falls from infinity to the stationary state $1$. (Rydberg constant $=1.097\times {10}^7 {\mathrm{m}}^{-1}$)

Consider the ground state of the $\mathrm{Cr}$ atom $\left(\mathrm{Z}=24\right)$. Determine the number of electrons with the azimuthal quantum numbers, $\mathrm{\ell }=1$ and $2$, respectively.

Determine uncertainity in the position of an electron (mass $=9.1\times {10}^{-31} \mathrm{Kg}$) moving with a velocity $300 \mathrm{m}.{\sec }^{-1}$, accurate upto $0.001\%.\left(\mathrm{h}=6.63\times {10}^{-34 }\mathrm{J}-\mathrm{s}\right)$