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Energy needed to seperate proton and electron - Physics Stack ...

Feb 19, 2018 ... It is found experimentally that 13.6 eV energy is required to separate a hydrogen atom into a proton and an electron. Compute the orbital radius ...

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ionization energy | Definition & Facts | Britannica

Ionization energy, in chemistry and physics, the amount of energy required to ... For a hydrogen atom, composed of an orbiting electron bound to a nucleus of one ... an ionization energy of 2.18 × 10⁻¹⁸ joule (13.6 electron volts) is required to ... The magnitude of the ionization energy of an element is dependent on the ...

For more information, see ionization energy | Definition & Facts | Britannica

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ionization energy | Definition & Facts | Britannica

Ionization energy, in chemistry and physics, the amount of energy required to ... For a hydrogen atom, composed of an orbiting electron bound to a nucleus of one ... an ionization energy of 2.18 × 10⁻¹⁸ joule (13.6 electron volts) is required to ... The magnitude of the ionization energy of an element is dependent on the ...

For more information, see ionization energy | Definition & Facts | Britannica

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Bohr Model of the Hydrogen Atom: Postulates, Energy Levels ...

Bohr Model of the hydrogen atom attempts to plug in certain gaps as ... atom, electron/s could revolve in stable orbits without emitting radiant energy. ... In this postulate, Bohr incorporated early quantum concepts into the atomic ... The state of the atom wherein the electron is revolving in the orbit of smallest Bohr radius (a 0) ...

For more information, see Bohr Model of the Hydrogen Atom: Postulates, Energy Levels ...

Given that

Measured in an experiment.

The energy needed to separate a hydrogen atom E = - 13.6 eV   

                         E = - 13.6 * 1.6 * 10^{-19} Joules                                                     \because 1 eV = 1.6 * 10^{-19} J

                         E = - 2.2 * 10^{-18} joules

Step 1: Calculating the radius of the electron

            The electron in a hydrogen atom has a total energy of E = - \frac{e^2}{8 \pi \epsilon_0 r}

            Where, Constant \frac{1}{4 \pi \epsilon_0} = 9.0 * 10^{9} N m^2/C ,  Charge of electron e = 1.6 * 10^{-19} C, r - radius of the electron

            Radius of the electron r = - \frac{e^2}{8\pi \epsilon_0 E}

                   r = -(\frac{1}{2*4\pi \epsilon_0}) \frac{(1.6 * 10^{-19})^2}{(- 2.2 * 10^{-18}) }

                   r = -(\frac{9 * 10^{9}}{2}) \frac{(1.6 * 10^{-19})^2}{(- 2.2 * 10^{-18}) }

                  r=5.3*10^{-11} m

               Radius of the electron in hydrogen atom  r = 5.3* 10^{11} m

Step 2: Determining the velocity of the electron in hydrogen atom

             The orbit radius and electron velocity are related in this equation.

                   r = \frac{e^2}{4\pi \epsilon_0 mv^2}       

                  v^2 = \frac{e^2}{4\pi \epsilon_0 m r}       

            Velocity of an electron v = \frac{e}{\sqrt{4 \pi \epsilon_0 m r}}

               Plug in the known values  

                   v = \frac{1.6* 10^{-19}}{\sqrt{\frac{9.1 * 10^{-31} * 5.3* 10^{11}}{9* 10^{9}}}}

                   v = 2.2 * 10^{6} m/s

            Therefore, velocity of the electron in hydrogen atom v = 2.2 * 10^{6} m/s