Question

In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If $${a_0}$$ is the radius of the ground state orbit, $$m$$ is the mass, $$e$$ is the charge on the electron and $${\varepsilon _0}$$ is the vacuum permittivity, the speed of the electron is

A. $$0$$
B. $$\frac{e}{{\sqrt {{\varepsilon _0}{a_0}m} }}$$
C. $$\frac{e}{{\sqrt {4\pi {\varepsilon _0}{a_0}m} }}$$  
D. $$\frac{{\sqrt {4\pi {\varepsilon _0}{a_0}m} }}{e}$$
Answer :   $$\frac{e}{{\sqrt {4\pi {\varepsilon _0}{a_0}m} }}$$
Solution :
Centripetal force = Coulombian force
$$\eqalign{ & \frac{{m{v^2}}}{{{a_0}}} = \frac{1}{{4\pi {\varepsilon _0}}}.\frac{{e \times e}}{{a_0^2}} \cr & \Rightarrow {v^2} = \frac{{{e^2}}}{{4\pi {\varepsilon _0}.{a_0}.m}} \cr & \Rightarrow v = \frac{e}{{\sqrt {4\pi {\varepsilon _0}.{a_0}.m} }} \cr} $$

Releted MCQ Question on
Modern Physics >> Atoms And Nuclei

Releted Question 1

If elements with principal quantum number $$n > 4$$  were not allowed in nature, the number of possible elements would be

A. 60
B. 32
C. 4
D. 64
Releted Question 2

Consider the spectral line resulting from the transition $$n = 2 \to n = 1$$    in the atoms and ions given below. The shortest wavelength is produced by

A. Hydrogen atom
B. Deuterium atom
C. Singly ionized Helium
D. Doubly ionised Lithium
Releted Question 3

An energy of $$24.6\,eV$$  is required to remove one of the electrons from a neutral helium atom. The energy in $$\left( {eV} \right)$$  required to remove both the electrons from a neutral helium atom is

A. 38.2
B. 49.2
C. 51.8
D. 79.0
Releted Question 4

As per Bohr model, the minimum energy (in $$eV$$ ) required to remove an electron from the ground state of doubly ionized $$Li$$ atom $$\left( {Z = 3} \right)$$  is

A. 1.51
B. 13.6
C. 40.8
D. 122.4

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