Embibe Experts Solutions for Exercise 4: Assignment

If the largest wavelength of a certain series of hydrogen spectrum is $1875 \mathrm{nm}$. Then smallest wavelength of that series will be

An $X$-ray tube operates at the voltage of $40 \mathrm{kV}.$ Find the ratio of the shortest wavelength of $X$-ray produced to the de-Broglie wavelength of the incident electron. The specific charge of the electron is $1.8\times {10}^{11}\mathrm{C} {\mathrm{kg}}^{–1}.$

Consider a hydrogen like atom whose energy in $n \mathrm{th}$ excited state is given by $E_n=-\frac{13.6Z^2}{n^2}.$ When this excited atom makes a transition from excited state to ground state, most energetic photons have energy $E_{\max }=52.224 \mathrm{eV}$ and least energetic photons have energy $E_{\min }=1.224 \mathrm{eV}.$ Find the state of excitation.

An ${\mathrm{He}}^{+}$ ion in ground state is fired towards a Hydrogen atom in ground state and at rest. The minimum kinetic energy in $\mathrm{eV}$ of ${\mathrm{He}}^{+}$ ion so that both single electron species may get excited is $x.$ The value of $x-166$ is

A hydrogen atom with its electron in the $n^{\mathrm{th}}$ orbit is ionized by electromagnetic radiation of wavelength $45 \mathrm{nm}.$ If the kinetic energy of the ejected electron is $26.75 \mathrm{eV}$ then the value of $n$ is $\left(hc=1242 \mathrm{eV} \mathrm{nm}\right)$

In hydrogen spectrum the shortest wavelength in the Balmer series is ${\lambda }_0.$ If largest wavelength in Lyman series for helium ion, is $\frac{{\lambda }_0}{k},$ then find value of $k.$

In hydrogen-like atom $\left(Z=11\right)$, $n^{\mathrm{th}}$ line of Lyman series has wavelength $\lambda$ equal to the de-Broglie's wavelength of electron in the level from which it originated. What is the value of $n?$

An electron in hydrogen like atom makes a transition from $n^{\mathrm{th}}$ orbit and emits radiations corresponding to Lyman series. If the de Broglie wavelength of electron in $n^{\mathrm{th}}$ orbit is equal to wavelength of the radiation emitted, value of $n$, is (The atomic number of atom is $11$)