Q. 183.9( 18 Votes )

# In a hydrogen ato

Answer :

Given,

The distance between electron-proton of hydrogen atom = 0.53 Å = 0.53 × 10^{-10}m

Charge on electron, q_{1} = - 1.6 × 10^{-19} C

Charge on proton, q_{2} = 1.6 × 10^{-19} C

(a) Potential energy at infinity is Zero.

Potential energy of a system,

= Potential energy at infinity – Potential energy at distance d

= 0 -

Where, ϵ_{0} = permittivity of space

and, =

∴ Potential energy,

⇒ V = -43.7 × 10^{-19} J

On converting into electron volts we get,

⇒

⇒ V = -27.2 eV

(∵ 1eV = 1.6 × 10^{-19} J)

(b) Given, Kinetic energy is half of the potential energy in (a).

∴ Kinetic energy, K = 0.5 × (27.2) = 13.6 eV

Thus, Total energy of electron = -27.2 + 13.6 = -13.6 eV

Amount of work require to free the electron, A = Increase in energy the electron.

∴ A = 0-(-13.6) = 13.6 eV

(c) If we take potential energy Zero at 1.06 Å separation, then the potential energy of the system,

P =

⇒P = -21.74 × 10^{-19} J

In electron volts, the potential energy is given as,

P = -13.585 eV.

(1eV = 1.6 × 10^{-19} J)

∴ The amount of work done to free the electron in this case,

W = -27.17- (-13.585) = -13.585 eV

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