If E1 E2 and E3 represent respectively the kinetic energy of an electron and an Alpha particle and a Proton each having same de Broglie wavelength then
Answers
Correct order of energy is E1> E3>E2. Hope it will help you.
Therefore, the Kinetic Energy of the electron is greater than the other two particles and the Kinetic Energy of the Alpha particle is the least among the three ( E₁ > E₃ > E₂ ).
Given:
Kinetic Energy of an electron = E₁
Kinetic Energy of an alpha particle = E₂
Kinetic Energy of a proton = E₃
All the particles have the same de Broglie wavelength
To Find:
The possible relation between E₁, E₂, E₃.
Solution:
We can simply solve this problem by using the following mathematical process.
Let us assume that,
Mass of an electron = m₁
Mass of an alpha particle = m₂
Mass of a proton = m₃
Kinetic Energy of particle E = 1/2 mv²
Where m = mass of the particle
v = velocity of the particle
De Broglie wavelength λ = hmv
Where h = Plancks Constant
From the De Broglie Wavelength formula velocity of the particle v = λ/mh
Now substituting the Velocity v value in the Kinetic Energy equation, we get,
⇒ E = ( mλ² )/2( m²h² )
In the above equation, after eliminating the constants we get the proportionality condition for E and m
⇒ E ∝ 1/m
Kinetic Energy is inversely proportional to the mass of the particle.
According to the mass,
Alpha particle > Proton > Electron
i.e, m₂ > m₃ > m₁
We know that Kinetic Energy is inversely proportional to the mass of the particle.
So, E₁ > E₃ > E₂
Therefore, the Kinetic Energy of the electron is greater than the other two particles and the Kinetic Energy of the Alpha particle is the least among the three ( E₁ > E₃ > E₂ ).
#SPJ2