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This is one of our many quizzes on Atomic physics. Click on this to access more such competitive quizzes on Modern Physics and Semiconductors.

Atomic physics Quiz 2

physics

 Let us assume that an electron is revolving around a nucleus in the fifth orbit of an atom. Will you be able to calculate the angular momentum of the electron? If yes, find out the value. 

 The angular momentum will be the integral multiple of $\dfrac{h}{2\pi }$. Substitute the values in the equation. 

The number of orbit in which the electron is revolving can be written as, $n=5$ The angular momentum can be found by the equation, $L=\dfrac{nh}{2\pi }$ Substituting the values in it, $L=\dfrac{5\times 6.626\times {{10}^{-34}}}{2\times 3.14} \\ \therefore L=5.3\text{ kg}{{\text{m}}^{2}}{{\text{s}}^{-1}}$

 Hari has found out that the electron revolves in a particular orbit with a velocity mentioned as $3.3\times {{10}^{6}}\text{ m}{{\text{s}}^{-1}}$. The radius of this specific orbit has been mentioned as $53\times {{10}^{-12}}\text{ }m$. What will be the frequency of the moving electron?

 The frequency of an electron will be the ratio of the velocity of electrons to the circumference of the orbit. 

  $\text{The frequency,} \\ \text{n}=\dfrac{\text{velocity of electrons}}{\text{circumference of orbit}} \\ \Rightarrow n=\dfrac{v}{2\pi r} \\ \Rightarrow n=\dfrac{3.3\times {{10}^{6}}}{2 \times \pi \times 53\times {{10}^{-12}}} \\ \Rightarrow n=0.099\times {{10}^{17}} \\ \therefore n=9.9\times {{10}^{15}}\text{ }Hz$

 The velocity of ${{n}^{th}}$orbit has been mentioned as $5.6\times {{10}^{-2}}\text{ }m{{s}^{-1}}$and the radius of the orbit has been given as $4\times {{10}^{-3}}\text{ }m$. Calculate the value of $n$ if an electron is revolving in this orbit.  

  The angular momentum will be the product of the mass, velocity and the radius of orbit. 

$\text{The angular momentum,} \\ L=mvr \\ \text{Substituting the equation of angular momentum,} \\ \Rightarrow \dfrac{nh}{2\pi }=mvr \\ \text{Rearranging,} \\ \Rightarrow n=\dfrac{2\pi mvr}{h} \\ \Rightarrow n=\dfrac{2\pi \times 9.1\times {{10}^{-31}}\times 5.6\times {{10}^{-2}} 4\times {{10}^{-3}} }{6.62\times {{10}^{-34}}} \\ \Rightarrow n=\dfrac{1266.048\times {{10}^{-36}}}{6.62\times {{10}^{-34}}} \\ \therefore n=2$

 Trisha took a muonic hydrogen atom which is having a mass about $207{{m}_{e}}$ which revolves around a proton. Find out the ratio of the radius of this atom to the Bohr radius. 

 The radius of an orbit will be inversely proportional to the mass of the atom according to Bohr’s atomic model energy. 

 $\text{According to Bohr }\!\!'\!\!\text{ s atomic model energy,} \\ r\propto \dfrac{1}{m} \\ \text{Comparing,} \\ \Rightarrow \dfrac{{{r}_{\mu }}}{{{r}_{e}}}=\dfrac{{{m}_{e}}}{{{m}_{\mu }}} \\ \text{Substituting the values,} \\ \Rightarrow \dfrac{{{r}_{\mu }}}{{{r}_{e}}}=\dfrac{{{m}_{e}}}{207{{m}_{e}}} \\ \therefore \dfrac{{{r}_{\mu }}}{{{r}_{e}}}=4.831\times {{10}^{-3}}$

 Teena when observing one atom in which an electron was revolving with a velocity $\text{2}\text{.8}\times {{10}^{8}}\text{ }m{{s}^{-1}}$in the ${{n}^{th}}$ orbit having radius $5\times {{10}^{-12}}\text{ }m$. What will be the mass of the electron in this atom? 

 The velocity of the revolving electron will be the ratio of the electric charge to the square root of the product of $4\pi $, permittivity, mass of electron and radius of orbit. 

 $\text{The equation of velocity of revolving electron,} \\ v=\dfrac{e}{\sqrt{4\pi {{\varepsilon }_{0}}mr}} \\ \text{Substituting the values,} \\ 2.8\times {{10}^{8}}=\dfrac{1.6\times {{10}^{-19}}}{\sqrt{4\pi {{\varepsilon }_{0}}\times m\times 5\times {{10}^{-12}}}} \\ \text{Rearranging the equation,} \\ m=\dfrac{1.6\times {{10}^{-19}}\times 1.6\times {{10}^{-19}}}{7.84\times {{10}^{16}}\times 4\pi {{\varepsilon }_{0}}\times 5\times {{10}^{-12}}} \\ \Rightarrow m=\dfrac{2.56\times {{10}^{-38}} \times 8.98\times {{10}^{9}}}{39.2\times {{10}^{4}}} \\ \therefore m=5.86\times {{10}^{-32}}\text{ }kg$