Question

if the angular momentum of an electron in a bohr orbit is 2h/π then the value of potential energy of electrone present in he+2 ions is

Answer 1

According to Bohr's theory ,
angular momentum is inegral multiple of h/2π
Means, angular momentum , L = nh/2π

Given, angular momentum of an electron in a Bohr's orbit is 2h/1
e.g., 2h/π = nh/2π
⇒ n = 4

Now, potential energy , P.E= -27.2 × Z²/n² eV
Where Z is atomic number.
Here, Z = 2 [ atomic number of He = 2 ] and n = 4
∴ P.E = -27.2 × (2)²/(4)²
= -27.2 × 4/16
= -27.2/4
= -6.8 eV

Hence, potential energy = -6.8 eV

Answer 2

The potential energy of electron in the given orbit is -3.4 eV.

The angular momentum of an electron in a Bohr orbit is:

L = nh / 2π

It is given that the electron has momentum 2h / π, hence n = 4.

The potential energy of the electron is given by the formula:

U = -13.6 x Z^2 / n^2
Z = 2
n = 4
Therefore U = -13.6 x 0.25 = -3.4 eV