Radius of Bohr's orbit in hydrogen atom can be calculated as
r=‌×‌ or
‌‌r=0.529×‌Å where,
n= number of the orbit
Z= atomic number
For hydrogen's third Bohr's orbit,
r3‌=0.529∵‌Å‌=9×0.529Å......(i)
Also
r2=0.529×(2)2 (Given, radius of second Bohr's orbit radius.)
r2=4×0.529 r2∕4=0.529.....(ii)
From Eqs. (i) and (ii),
r3=9×‌⇒r3=‌r2 Hence, radius of third Bohr's orbit
=‌r2Energy of
nth Bohr's orbit is given as
En=‌ where,
n= number of orbit,
Z= atomic number [For hydrogen,
Z=1 ]
∴‌‌E2=k‌ [Given, second Bohr's orbit energy.]
k=E2×4 E2=k∕4.......(iii)
Also,
‌‌E3=k‌=‌.....(iv)
From Eqs. (iii) and (iv),
E3=‌⇒E3=‌E2 Hence, energy of third Bohr's orbit is
‌E2.