Q. using de Broglie hypothesis explain with the help of suitable diagram bohar second postulate of quantization of energy level in hydrogen atom and the ground state energy of hydrogen atom is - 13.6 eV.what are the Kinetic and potential energies of the electron in this state .
Answers
Answer:
De broglie assumed that electrons move in circular orbit with it mean position of vibration at periphery of assumed orbit. So assuming electron move like wave up down on a circular orbit we can say total periphery of that circular orbit will be equal to integral times of wavelength of vibration that is n×λ
Eqauting this we get n×λ = 2πr , where r is the radius of desire orbit
So λ= 2πr/n
Again as we know λ = h/p , where p is liner momentum (m c squared space equals fraction numerator h c over denominator lambda end fraction space
p space equals h over lambda)
From these two equation we can get the value of radius
And once value of radius is known we can find the energy of the orbit with desire radius from cuolombs law of electrostatic.
For diagram please refer NCERT book.
a) as per de Broglie relation
lemda = h/ mv
2πr= n× lemda
= n h/ mv
mvr = L
= nh/ 2π
b) K.E. = 13.6eV
P.E.= -27.2eV
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