Embibe Experts Solutions for Chapter: Modern Physics - I, Exercise 2: Exercise#2

A photon of wavelength $\lambda$ is absorbed by an electron confined to a box of length $\sqrt{\frac{35h\lambda }{8mc}}$. As a result, the electron makes a transition from state, $k=1$ to the state $n$. Subsequently, the electron transits from the state $n$ to the state $m$ by emitting a photon of wavelength, ${\lambda }^{\text{'}}=1.75\lambda$. Then,

The magnitude of acceleration of the electron in the $n^{\text{th}}$ orbit of hydrogen atom is $a_{\mathrm{H}}$ and that of singly ionised helium atom is $a_{\mathrm{He}}$. The ratio $a_{\mathrm{H}}:a_{\mathrm{He}}$ is,

A carrot looks orange in colour because of the $\beta$ carotene molecule in it. This means that the $\beta$ carotene molecule absorbs light of wavelengths,

An electron in an electron microscope with initial velocity $v_0\hat{\mathrm{i}}$ enters a region of a stray transverse electric field $E_0\hat{\mathrm{j}}$. The time taken for the change in its de-Broglie wavelength from the initial value of $\lambda$ to $\frac{\lambda }{3}$ is proportional to,

A particle of mass $m$ moves around the origin in a potential $\frac{1}{2}m{w}^2{r}^2$, where $r$ is the distance from the origin. Applying the Bohr model in this case, the radius of the particle in its $n^{\text{th }}$ orbit in terms of $a=\sqrt{h/\left(2\pi m\omega \right)}$ is,

To calculate the size of a hydrogen anion using the Bohr model, we assume that its two electrons move in an orbit such that they are always on diametrically opposite sides of the nucleus. With each electron having the angular momentum, $\overline{h}=\frac{h}{2\pi }$ and taking electron interaction into account, the radius of the orbit in terms of the Bohr radius of hydrogen atom, $a_{\mathrm{B}}=\frac{4\pi {\epsilon }_0 h^2}{m{e}^2}$ is,

Using the Heisenberg uncertainty principle, arrange the following particles in the order of increasing the lowest energy possible
$\left(\mathrm{I}\right)$ an electron in ${\mathrm{H}}_2$ molecule

$\left(\mathrm{II}\right)$ a $\mathrm{H}$ atom in a ${\mathrm{H}}_2$ molecule

$\left(\mathrm{III}\right)$ a proton in the carbon nucleus

$\left(\mathrm{IV}\right)$ a ${\mathrm{H}}_2$ molecule within a nanotube

The Hitomi satellite recently observed the Lyman alpha emission line $(n=2 \text{to} n=1)$ of Hydrogen-like iron ion (atomic number of iron is $26$) from the Perseus galaxy cluster. The wavelength of the line is closest to,