Question

11
Derive an expression relating radius of the atom to the mass, charge a
orbit number of the electron.
Calculate the radius of the third orbit in hydrogen atom using Bohr's
theory.
Derive an expression useful in calculating the energy of an electron in
n th orbit of hydrogen ​

Answer 1

Answer:

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