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  • Using Bohr’s atomic model, derive the expression for the velocity of electron revolving in the nth orbit of hydrogen atom.  

Using Bohr’s atomic model, derive the expression for the velocity of electron revolving in the nth orbit of hydrogen atom.

 

Answers (1)

According to Bohr's postulates, 

L_n=mv_nr_n=\frac{nh}{2\pi }

L_n\rightarrow  Angular momentum

v_n\rightarrow Speed of moving electron in the orbit

r_n\rightarrow radius of n^{th} orbit

h\rightarrow Planck's constant

m\rightarrow mass of particle

For a dynamically stable orbit in a hydrogen atom, 

F_e=F_c

 \\\frac{mv_n^2}{r_n}=\frac{1}{4\pi \epsilon _0}\frac{e^2}{r_n^2}

mv_n^2r_n=ke^2

By Bhors postulate

mvr=\frac{nh}{2\pi}

Therefore

\\\frac{nh}{2\pi}v_n=ke^2\\v_n=\frac{2\pi ke^2}{nh}

v_n=\frac{2\pi e^2}{4\pi\epsilon_0 nh}

v_n=\frac{ e^2}{2\epsilon_0 nh}

Posted by

Safeer PP

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