We need to consider no change in the temperature of gas (isothermal transformation)
Volume and pressure are inversely proportional magnitudes, so we can write:
Answer:
Given:
Thermal Kinetic Energy of an electron, 
= Boltzmann's constant
Temperature, T = 1800 K
Solution:
Now, to calculate the de-Broglie wavelength of the electron,
:

(1)
where
h = Planck's constant = 
= momentum of an electron
= velocity of an electron
= mass of electon
Now,
Kinetic energy of an electron = thermal kinetic energy



(2)
Using eqn (2) in (1):

Now, to calculate the de-Broglie wavelength of proton,
:

(3)
where
= mass of proton
= velocity of an proton
Now,
Kinetic energy of a proton = thermal kinetic energy



(4)
Using eqn (4) in (3):

The kinetic energy of the electron is

where

is the mass of the electron and v its speed. Since we know the value of the kinetic energy,

, we can find the value of the speed v:
To solve this problem we will use the kinematic equations of angular motion, starting from the definition of angular velocity in terms of frequency, to verify the angular displacement and its respective derivative, let's start:



The angular displacement is given as the form:
In the equlibrium we have to
and in the given position we have to

Derived the expression we will have the equivalent to angular velocity

Replacing,

Finally

Therefore the maximum angular displacement is 9.848°