TS EAMCET 19-July-2022 Shift 2 Solved Paper

Radius of Bohr's orbit in hydrogen atom can be calculated as r=‌

n2h2

4π2me2

×‌

1

Z

or ‌‌r=0.529×‌

n2

Z

Å
where, n= number of the orbit
Z= atomic number
For hydrogen's third Bohr's orbit,
r3‌=0.529∵‌

(3)2

1

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×‌

r2

4

⇒r3=‌

9

4

r2
Hence, radius of third Bohr's orbit =‌

9

4

r2
Energy of nth Bohr's orbit is given as
En=‌

kZ2

n2

where, n= number of orbit,
Z= atomic number [For hydrogen, Z=1 ]
∴‌‌E2=k‌

(1)2

(2)2

[Given, second Bohr's orbit energy.]
k=E2×4
E2=k∕4.......(iii)
Also, ‌‌E3=k‌

(1)2

(3)2

=‌

k

9

.....(iv)
From Eqs. (iii) and (iv),
E3=‌

E2×4

9

⇒E3=‌

4

9

E2
Hence, energy of third Bohr's orbit is ‌

4

9

E2.