Sahana Ansari and Neha Miglani Solutions for Chapter: Structure of Atom, Exercise 4: Chapter Practice

In the ultraviolet region of atomic spectrum of hydrogen, a line is obtained at $1050 \mathrm{\AA }$. Calculate the energy of one million photons of this wavelength.

The wavelength of first spectral line in the Balmer series is $6561 \mathrm{\AA }$. Calculate the wavelength of the second spectral line in Balmer series.

When a certain metal was irradiated with a light of frequency $3.2\times {10}^{16} \mathrm{Hz}$, the photoelectrons had twice the kinetic energy as emitted when the same metal was irradiated with light of frequency $2.0\times {10}^{16} \mathrm{Hz}$. Calculate the threshold frequency $\left({\mathrm{v}}_0\right)$ of the metal.

What is the energy in joules required to excite the electron of the hydrogen from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is $-2.18\times {10}^{-11}$ ergs.

The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particle. Justify the statement with the help of a suitable example.

Calculate the velocity condition for the wavelength associated with a moving electron to be equal to the wavelength associated with a moving proton. (Mass of electron$=9.11\times {10}^{-28} \mathrm{g}$; Mass of proton$=1.67\times {10}^{-24} \mathrm{g}$; $\mathrm{h}=6.6\times {10}^{-34} \mathrm{Js}; \mathrm{J}\equiv {\mathrm{kgm}}^2{\mathrm{s}}^{-2}$)

Why is $+2$ oxidation state of $\mathrm{Mn} \left(25\right)$ quite stable, while the same is not true for iron $\left(26\right)$?

What is meant by dual nature of electrons? Calculate the energy and wavelength of the photon emitted by hydrogen atom when electron makes a transition from $\mathrm{n}=2$ to $\mathrm{n}=1$. Given that the ionisation potential is $13.6 \mathrm{eV}$ ($1\mathrm{eV}=1.6\times {10}^{-19} \mathrm{J}$).