I E Irodov Solutions for Chapter: ATOMIC AND NUCLEAR PHYSICS, Exercise 3: PROPERTIES OF ATOMS. SPECTRA

How many elements are there in a row between those whose wavelengths of $K_{\mathrm{\alpha }}$ lines are equal to $250$ and $179 \mathrm{pm}$?

$R$ is the Rydberg's constant ($R=1.097\times {10}^7 {\mathrm{m}}^{-1}$), speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$.

Find the voltage applied to an $\mathrm{X}$-ray tube with nickel anticathode, if the wavelength difference between the $K_{\mathrm{\alpha }}$ line and the short-wave cut-off of the continuous $\mathrm{X}$-ray spectrum is equal to $84 \mathrm{pm}.$ 

$R$ is the Rydberg's constant ($R=1.097\times {10}^7 {\mathrm{m}}^{-1}$), Planck's constant $h=6.626\times {10}^{-34} \mathrm{J} {\mathrm{Hz}}^{-1}$, speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$, charge of electron $e=1.66\times {10}^{-19} \mathrm{C}$

At a certain voltage applied to an $\mathrm{X}$-ray tube with aluminium anticathode, the short-wave cut-off wavelength of the continuous $\mathrm{X}$-ray spectrum is equal to $0.50 \mathrm{nm}$. Will the $K$ series of the characteristic spectrum, whose excitation potential is equal to $1.56 \mathrm{kV}$, be also observed in this case?

charge on electron is $e=1.6\times {10}^{-19} \mathrm{C}$, Plank's constant $h=6.626\times {10}^{-34} \mathrm{J} {\mathrm{Hz}}^{-1}$, speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$.

When the voltage applied to an $\mathrm{X}$-ray tube increased from $V_1=10 \mathrm{kV}$ to $V_2=20 \mathrm{kV},$ the wavelength interval between the $K_{\mathrm{\alpha }}$ line and the short-wave cut-off of the continuous $\mathrm{X}$-ray spectrum increases by a factor $n=3.0.$ Find the atomic number of the element of which the tube's anticathode is made.

charge of an electron is $e=1.6\times {10}^{-19} \mathrm{C}$, $R$ is the Rydberg's constant ($R=1.097\times {10}^7 {\mathrm{m}}^{-1}$), Planck's constant $h=6.626\times {10}^{-34} \mathrm{J} {\mathrm{Hz}}^{-1}$, speed of light $3\times {10}^8 \mathrm{m} s^{-1}$.

Which metal has, in its absorption spectrum, the difference between the frequencies of $\mathrm{X}$-ray $K$ and $L$ absorption edges equal to $\mathrm{\Delta }\omega =6.85\times {10}^{18} {\mathrm{s}}^{-1}$?

$R$ is the Rydberg's constant ($R=1.097\times {10}^7 {\mathrm{m}}^{-1}$).

Calculate the binding energy of a $K$ electron in vanadium, whose $L$ absorption edge has the wavelength ${\lambda }_{\mathrm{L}}=2.4 \mathrm{nm}.$

Atomic number of vanadium $Z=23$, $R$ is the Rydberg's constant ($R=1.097\times {10}^7 {\mathrm{m}}^{-1}$), Planck's constant $h=6.626\times {10}^{-34} \mathrm{J} {\mathrm{Hz}}^{-1}$, speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$.

Find the binding energy of an $L$ electron in titanium, if the wavelength difference between the first line of the $K$ series and its short wave cut-off is $\mathrm{\Delta }\lambda =26 \mathrm{pm}$.

Atomic number of titanium $Z=22$, $R$ is the Rydberg's constant ($R=1.097\times {10}^7 {\mathrm{m}}^{-1}$), Planck's constant $h=6.626\times {10}^{-34} \mathrm{J} {\mathrm{Hz}}^{-1}$, speed of light $c=3\times {10}^8 \mathrm{m} s^{-1}$.

Find the kinetic energy and the velocity of the photoelectrons liberated by $K_{\mathrm{\alpha }}$ radiation of zinc from the $K$ shell of iron, whose $K$ band absorption edge wavelength is ${\lambda }_{\mathrm{K}}=174 \mathrm{pm}$.

Atomic number of zinc $Z=30$, $R$ is the Rydberg's constant ($R=1.097\times {10}^7 {\mathrm{m}}^{-1}$), Planck's constant $h=6.626\times {10}^{-34} \mathrm{J} {\mathrm{Hz}}^{-1}$, speed of light $c=3\times {10}^8 \mathrm{m} s^{-1}$.