Question

application of bohr's theory inderivation of energy of an orbit

Answer 1

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Let e, m and v be respectively the charge, mass and velocity of the electron and r the radius of the orbit. The positive charge on the nucleus is Ze, where Z is the atomic number (in case of hydrogen atom Z = 1). As the centripetal force is provided by the electrostatic force of attraction. We have

r

mv

2

=

4πε

0

1

r

2

(Ze)×e

mv

2

=

4πε

0

r

Ze

2

....(i)

From the first postulate, the angular momentum of the electron is

mvr=n

2π

h

....(ii)

where n (= 1, 2, 3, ...) is quantum number. Squaring eq. (ii) and dividing by eq. (i), we

get

r=n

2

πmZe

2

h

2

ε

0

Z=1

Since

r=n

2

πme

2

h

2

ε

0