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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** ...

For more information, see **Energy needed** to seperate **proton** and **electron** - Physics Stack ...

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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

I found an answer from www.britannica.com

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