Suppose potential energy between electron n proton at distance "r" is given by... (-ke^2)/(3.R^3)...Use bohr's theory to obtain energy levels of such hypothetical atom
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Since H atom is a bounded system U cannot be positive
U = - ke2/3r3
Electrostatic force of attraction at a distance r will be
F = -dU/dr
= -ke2/r4
Assuming a circular radius of the orbit
mv2/r = ke2/r4
=> mv2 = ke2/r3
=> ½mv2 = ke2/2r3
=> KE = ke2/2r3
E = KE + U
= ke2/2r3 + (- ke2/3r3)
= ke2/6r3
Gives the energy level of the atom
U = - ke2/3r3
Electrostatic force of attraction at a distance r will be
F = -dU/dr
= -ke2/r4
Assuming a circular radius of the orbit
mv2/r = ke2/r4
=> mv2 = ke2/r3
=> ½mv2 = ke2/2r3
=> KE = ke2/2r3
E = KE + U
= ke2/2r3 + (- ke2/3r3)
= ke2/6r3
Gives the energy level of the atom
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1
Answer:
n^h^6/384m^3k^2e^4pi^6
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