Question

An electron in a hydrogen atom has an energy of -3.4 eV. The difference between its kinetic and potential energy is ______.

Options

• 10.2 eV

• -10.2 eV

• -13.6 eV

• Both 10.2 eV and -10.2 eV

Answer 1

An electron in a hydrogen atom has an energy of -3.4 eV. The difference between its kinetic and potential energy is both 10.2 eV and -10.2 eV.

Explanation:

According to Bohr's model, the kinetic energy of a moving electron in the nth orbit is given as

K = `(Rhc)/n^2` ......(i)

where, R = Rydberg constant, h = Planck's constant and c = speed of light.

Similarly, the potential energy of an electron moving in the nth orbit,

P = `-2(Rhc)/n^2` .........(ii)

From Eqs. (i) and (ii), we have

P = -2K

The total energy of the electron moving in the nth orbit,

E = K + P = K - 2K

E = -K

⇒ K = -E = -(-3.4 eV) [given, E = -3.4 eV]

⇒ K = 3.4 eV

From Eq. (iii), we have

P = -2K = -2(3.4) = -6.8 eV

∵ P - K = -6.8 - 3.4 = -10.2 eV

and K - P = 3.4 - (-6.8) = 10.2 eV