DC Pandey Solutions: Modern Physics I- 3 | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


¢ Objective Questions (Level 2)
1. F F
a c
= Þ 
GmM
r
mv
r
2
2
= …(i)
and mvr
nh
=
2p
 …(ii)
From Eq. (ii)
Þ v
nh
mr
=
2p
Putting this value in Eq. (i)
GM
r
h h
m r
=
2 2
2 2 2
4p
 
Þ r
n h
m GM
=
2 2
2 2
4 p
KE = =
´
=
1
2
1
2 2
2
mv
m GM
r
GMm
r
PE =
- GMm
r
Þ E = + KE PE
Þ E
GMm
r
GMm m GM
n h
=
-
=
- ´
2
4
2
2 2
2 2
p
Þ E
G M m
n h
=
-2
2 2 2 3
2 2
p
 for ground state n = 1
Þ E
G M m
n
=
- 2
2 2 2 3
2
p
Hence correct option is (b).
2. We have m p
n n n
n
n
i A
e
T
r = = ´
2
Þ m
p
p
n
n n
n
n n
e r u
r
eu r
=
´ ´ ´
=
2
2 2
Þ m
n
e
v
n
r n ev r
n = ´ ´
´
= ´
1 1
2
1 1
2 2
Þ m
2
1 1
2
2
=
´ ev r
and m
1
1 1
2
1 = ´
ev r
Þ m
m
1
2
2
=
Hence magnetic moment decreases two
times correct option is (b).
3. For H-like atom E
n
n
=
- (13.6)Z eV
2
2
Here E
z
2
2
4
=
-(13.6)
 and E z
1
2
= - 13.6
E E
2 1
- = 40.8 eV
Þ 13.6 40.8 Z
2
1
1
4
´ -
é
ë
ê
ù
û
ú
=
Þ Z
2
408 4
13 6 3
=
´
´
Þ
.
.
 Z
2
4 =
Þ   Z = 2
Energy needed to remove the electron from
ground state is 
- = + ´ = + ´ = E Z
1
2
4 ( ) 13.6 13.6 54.4 eV
Hence correct option is (a).
i
e
T
e
r
u
ev
r
n
n
n
n
n
n
= = =
2
2
p
p
Q u
n
n
µ
1
 and r
n
n
µ
1
2
Þ i
n
n
µ
1
3
 Þ 
i
i
2
1
3
1
2
=
Þ i i
1 2
8 =
Hence current increases 8 times correct
option is (c).
5. Since five dark lines are pos si ble hence atom 
is ex cited to n = 6 state.
The number of transition in emission line 
=
- n n ( ) 1
2
Number of emission transition =
´
=
6 5
2
15
Hence correct option is (c).
6. A r
n n
= p
2
 for hydrozen atom r kn
n
=
2
where k is constant.
Þ A k n
n
= p
2 4
Þ A k
1
2
= p µ 
A
A
n
n
1
4
=
 75
Page 2


¢ Objective Questions (Level 2)
1. F F
a c
= Þ 
GmM
r
mv
r
2
2
= …(i)
and mvr
nh
=
2p
 …(ii)
From Eq. (ii)
Þ v
nh
mr
=
2p
Putting this value in Eq. (i)
GM
r
h h
m r
=
2 2
2 2 2
4p
 
Þ r
n h
m GM
=
2 2
2 2
4 p
KE = =
´
=
1
2
1
2 2
2
mv
m GM
r
GMm
r
PE =
- GMm
r
Þ E = + KE PE
Þ E
GMm
r
GMm m GM
n h
=
-
=
- ´
2
4
2
2 2
2 2
p
Þ E
G M m
n h
=
-2
2 2 2 3
2 2
p
 for ground state n = 1
Þ E
G M m
n
=
- 2
2 2 2 3
2
p
Hence correct option is (b).
2. We have m p
n n n
n
n
i A
e
T
r = = ´
2
Þ m
p
p
n
n n
n
n n
e r u
r
eu r
=
´ ´ ´
=
2
2 2
Þ m
n
e
v
n
r n ev r
n = ´ ´
´
= ´
1 1
2
1 1
2 2
Þ m
2
1 1
2
2
=
´ ev r
and m
1
1 1
2
1 = ´
ev r
Þ m
m
1
2
2
=
Hence magnetic moment decreases two
times correct option is (b).
3. For H-like atom E
n
n
=
- (13.6)Z eV
2
2
Here E
z
2
2
4
=
-(13.6)
 and E z
1
2
= - 13.6
E E
2 1
- = 40.8 eV
Þ 13.6 40.8 Z
2
1
1
4
´ -
é
ë
ê
ù
û
ú
=
Þ Z
2
408 4
13 6 3
=
´
´
Þ
.
.
 Z
2
4 =
Þ   Z = 2
Energy needed to remove the electron from
ground state is 
- = + ´ = + ´ = E Z
1
2
4 ( ) 13.6 13.6 54.4 eV
Hence correct option is (a).
i
e
T
e
r
u
ev
r
n
n
n
n
n
n
= = =
2
2
p
p
Q u
n
n
µ
1
 and r
n
n
µ
1
2
Þ i
n
n
µ
1
3
 Þ 
i
i
2
1
3
1
2
=
Þ i i
1 2
8 =
Hence current increases 8 times correct
option is (c).
5. Since five dark lines are pos si ble hence atom 
is ex cited to n = 6 state.
The number of transition in emission line 
=
- n n ( ) 1
2
Number of emission transition =
´
=
6 5
2
15
Hence correct option is (c).
6. A r
n n
= p
2
 for hydrozen atom r kn
n
=
2
where k is constant.
Þ A k n
n
= p
2 4
Þ A k
1
2
= p µ 
A
A
n
n
1
4
=
 75
Taking log both sides log log
A
A
n
n
1
4
æ
è
ç
ç
ö
ø
÷
÷
=
Hence it is a straight line with slope = 4
Correct option is (b)
7. For hydrogen atom i
n
n
µ
1
3
 and
  B
i
r
n
n
n
µ µ B k
n
n
=
1
5
[ ] Q r n
n
´
2
Þ B
k
2
5
2
= and B k
1
=
Þ 
B
B
2
1
5
1
2
1
32
= =
Þ B B
1 2
32 =
Hence magnatic field increases 32 times.
The correct option is (d).
8. For H-atom Lyman se ries is given by
1 1
1
1
2 2
l
= -
é
ë
ê
ù
û
ú
R
n
 for first line n = 2
Þ 
1
1
1
2
2
l
= -
é
ë
ê
ù
û
ú
R
Þ 
1 3
4 l
=
R
Momentum of photon P
h
p
=
l
Let momentum of atom p
A
Q Initial momentum was zero. Hence using
momentum conservation law, we get
p p
A B
= Þ Mv
h hR
= =
l
3
4
Þ     v
hR
M
=
3
4
Hence the correct option is (a).
9. Light wave equation is 
200 10
15 1
V/m 1.5 sec sin ( ) ´
-
t
´ ´
-
cos ( ) 0.5 sec 10
15 1
t
Here maximum frequency =
´ 1.5 10
2
15
p
Maxmum incident energy 
=
´
´
´
´
-
-
1.5 6.6
1.6
10
2
10
10
15 34
19
p
= 0.98 eV
Since work function = > 2eV maximum
energy hence no emission of electrons.
Thus correct option is (d).
10. Since in Balmer se ries of H-like atom
wave lengths (in  vis i ble re gion) are found
same or smaller hence the gas was ini tially
in sec ond ex cited state.
Cor rect op tion is (c).
11. For H-atom T n
H
= 2
3
p
and for H-like atom
T
n
z
x
=
2
3
2
p
For H-atom in ground state T
H
= 2p
For H-like atom in first excited state
   T
z z
x
=
´
=
´ ( ) 2 2 2 8
3
2 2
p p
But T T
H x
= 2 Þ 2
2 2 8
2
p
p
=
´ ´
z
Þ z
2
16 = 
Þ z = 4
Hence correct option is (c).
12. For K
a
 line of X-ray
1
1
2
2
l
= -
a
c
z ( )
Q z (atomic No.) for Pb Pb Pb
204 206 208
, ,
are same hence l l l
1 2 3
= = .
Hence correct option is (c).
13. The cor rect op tion is (d).
14. Since E
n
n
=
-13.6 eV
2
Þ E
1
= - 13.6 eV
and first excited state E
2
4
=
-13.6
eV
76
Page 3


¢ Objective Questions (Level 2)
1. F F
a c
= Þ 
GmM
r
mv
r
2
2
= …(i)
and mvr
nh
=
2p
 …(ii)
From Eq. (ii)
Þ v
nh
mr
=
2p
Putting this value in Eq. (i)
GM
r
h h
m r
=
2 2
2 2 2
4p
 
Þ r
n h
m GM
=
2 2
2 2
4 p
KE = =
´
=
1
2
1
2 2
2
mv
m GM
r
GMm
r
PE =
- GMm
r
Þ E = + KE PE
Þ E
GMm
r
GMm m GM
n h
=
-
=
- ´
2
4
2
2 2
2 2
p
Þ E
G M m
n h
=
-2
2 2 2 3
2 2
p
 for ground state n = 1
Þ E
G M m
n
=
- 2
2 2 2 3
2
p
Hence correct option is (b).
2. We have m p
n n n
n
n
i A
e
T
r = = ´
2
Þ m
p
p
n
n n
n
n n
e r u
r
eu r
=
´ ´ ´
=
2
2 2
Þ m
n
e
v
n
r n ev r
n = ´ ´
´
= ´
1 1
2
1 1
2 2
Þ m
2
1 1
2
2
=
´ ev r
and m
1
1 1
2
1 = ´
ev r
Þ m
m
1
2
2
=
Hence magnetic moment decreases two
times correct option is (b).
3. For H-like atom E
n
n
=
- (13.6)Z eV
2
2
Here E
z
2
2
4
=
-(13.6)
 and E z
1
2
= - 13.6
E E
2 1
- = 40.8 eV
Þ 13.6 40.8 Z
2
1
1
4
´ -
é
ë
ê
ù
û
ú
=
Þ Z
2
408 4
13 6 3
=
´
´
Þ
.
.
 Z
2
4 =
Þ   Z = 2
Energy needed to remove the electron from
ground state is 
- = + ´ = + ´ = E Z
1
2
4 ( ) 13.6 13.6 54.4 eV
Hence correct option is (a).
i
e
T
e
r
u
ev
r
n
n
n
n
n
n
= = =
2
2
p
p
Q u
n
n
µ
1
 and r
n
n
µ
1
2
Þ i
n
n
µ
1
3
 Þ 
i
i
2
1
3
1
2
=
Þ i i
1 2
8 =
Hence current increases 8 times correct
option is (c).
5. Since five dark lines are pos si ble hence atom 
is ex cited to n = 6 state.
The number of transition in emission line 
=
- n n ( ) 1
2
Number of emission transition =
´
=
6 5
2
15
Hence correct option is (c).
6. A r
n n
= p
2
 for hydrozen atom r kn
n
=
2
where k is constant.
Þ A k n
n
= p
2 4
Þ A k
1
2
= p µ 
A
A
n
n
1
4
=
 75
Taking log both sides log log
A
A
n
n
1
4
æ
è
ç
ç
ö
ø
÷
÷
=
Hence it is a straight line with slope = 4
Correct option is (b)
7. For hydrogen atom i
n
n
µ
1
3
 and
  B
i
r
n
n
n
µ µ B k
n
n
=
1
5
[ ] Q r n
n
´
2
Þ B
k
2
5
2
= and B k
1
=
Þ 
B
B
2
1
5
1
2
1
32
= =
Þ B B
1 2
32 =
Hence magnatic field increases 32 times.
The correct option is (d).
8. For H-atom Lyman se ries is given by
1 1
1
1
2 2
l
= -
é
ë
ê
ù
û
ú
R
n
 for first line n = 2
Þ 
1
1
1
2
2
l
= -
é
ë
ê
ù
û
ú
R
Þ 
1 3
4 l
=
R
Momentum of photon P
h
p
=
l
Let momentum of atom p
A
Q Initial momentum was zero. Hence using
momentum conservation law, we get
p p
A B
= Þ Mv
h hR
= =
l
3
4
Þ     v
hR
M
=
3
4
Hence the correct option is (a).
9. Light wave equation is 
200 10
15 1
V/m 1.5 sec sin ( ) ´
-
t
´ ´
-
cos ( ) 0.5 sec 10
15 1
t
Here maximum frequency =
´ 1.5 10
2
15
p
Maxmum incident energy 
=
´
´
´
´
-
-
1.5 6.6
1.6
10
2
10
10
15 34
19
p
= 0.98 eV
Since work function = > 2eV maximum
energy hence no emission of electrons.
Thus correct option is (d).
10. Since in Balmer se ries of H-like atom
wave lengths (in  vis i ble re gion) are found
same or smaller hence the gas was ini tially
in sec ond ex cited state.
Cor rect op tion is (c).
11. For H-atom T n
H
= 2
3
p
and for H-like atom
T
n
z
x
=
2
3
2
p
For H-atom in ground state T
H
= 2p
For H-like atom in first excited state
   T
z z
x
=
´
=
´ ( ) 2 2 2 8
3
2 2
p p
But T T
H x
= 2 Þ 2
2 2 8
2
p
p
=
´ ´
z
Þ z
2
16 = 
Þ z = 4
Hence correct option is (c).
12. For K
a
 line of X-ray
1
1
2
2
l
= -
a
c
z ( )
Q z (atomic No.) for Pb Pb Pb
204 206 208
, ,
are same hence l l l
1 2 3
= = .
Hence correct option is (c).
13. The cor rect op tion is (d).
14. Since E
n
n
=
-13.6 eV
2
Þ E
1
= - 13.6 eV
and first excited state E
2
4
=
-13.6
eV
76
Þ                     E
2
= - 3.4 eV 
         DE E E = - =
2 1
10.2 if K < 10.2 eV
The electron collide elastically with H-atom 
in ground state.
The correct option is (c).
15. For Lyman se ries 
1 1
1
1
2 2
l
= -
é
ë
ê
ù
û
ú
R
n
 here n = 3
Þ 
1
1
1
9 l
= -
é
ë
ê
ù
û
ú
R 
Þ
1 8
9 l
=
R
P
h Rh
photon
= =
l
8
9
But P P
Photon H-atom
=
Þ 
8
9
Rh
M v
p
= ´
Þ v =
´ ´ ´ ´
´ ´ ´
-
-
8 10 10
9 10
7 34
31
1.097 6.6
1837 9.1
Þ v = 4 m/s
Hence correct option is (a).
16. Power = = ´ ´ ´ =
-
VI 150 10 10 10 1500
3 3
W
The 99% power heated the target hence
Heating power = ´ = ´
99
100
1500 15 99 W
The rate at which target is heated per sec.
(in cal)
   =
´
-
15 99
355
4.2
~
 Q1
1
J
4.2
cal =
é
ë
ê
ù
û
ú
Hence correct option is (c).
17. E
z
n
n
= -
´ 13.6 eV
2
2
E z
3
2
9
= -
13.6 eV
 and E z
4
2
16
=
-13.6 eV
DE E E z = - = ´ -
é
ë
ê
ù
û
ú
4 3
2
1
9
1
16
( ) 13.6 eV
Þ DE =
´ ´
´
=
13.6 eV)
32.4 eV
( 2 7
16 9
2
Þ z
2
9
7
49 =
´ ´
´
=
16 32.4
13.6
Þ z = 7
Hence correct option is (d).
18. l = = =
h
p
h
m K
h
m eV
p p
2 2
 
Þ 
10
10
2 1836 10 10
13
34
31 19
-
-
- -
=
´
´ ´ ´ ´ ´ ´
6.6
9.1 1.6 V
Þ V = ´ 8.15 volt 10
4
Hence correct option is (b).
19. Since E
n
n
µ
1
2
 and L n
n
µ
Hence E
L
n
n
µ
1
2
The correct option is (d).
20. Since m
p
n
n n
eu r
=
2
 Q u
n
n
µ
1
  and r n
n
µ
2
Þ m
n
kn =
Where k is constant for H-atom
For ground state m
1
1 = ´ = k k …(i)
For third excited state n = 4
m
2
4 4 = ´ = k k …(ii)
From Eqs. (i) and (ii) we get m m
2 1
4 =
Hence correct option is (d).
21. By con ser v a tion of mo men tum
M v M M v
H H H
= + ¢ ( ) Þ v
v
¢ =
2
Let initial KE of H-atom = K
Final KE of each-H-atom =
K
2
For excitation 
K
E E
2 4
2 1
= - =
-
+
13.6
13.6
Þ 
K
2
= 10.2 eV
Þ K = 20.4 eV
Hence correct option is (a).
 77
Page 4


¢ Objective Questions (Level 2)
1. F F
a c
= Þ 
GmM
r
mv
r
2
2
= …(i)
and mvr
nh
=
2p
 …(ii)
From Eq. (ii)
Þ v
nh
mr
=
2p
Putting this value in Eq. (i)
GM
r
h h
m r
=
2 2
2 2 2
4p
 
Þ r
n h
m GM
=
2 2
2 2
4 p
KE = =
´
=
1
2
1
2 2
2
mv
m GM
r
GMm
r
PE =
- GMm
r
Þ E = + KE PE
Þ E
GMm
r
GMm m GM
n h
=
-
=
- ´
2
4
2
2 2
2 2
p
Þ E
G M m
n h
=
-2
2 2 2 3
2 2
p
 for ground state n = 1
Þ E
G M m
n
=
- 2
2 2 2 3
2
p
Hence correct option is (b).
2. We have m p
n n n
n
n
i A
e
T
r = = ´
2
Þ m
p
p
n
n n
n
n n
e r u
r
eu r
=
´ ´ ´
=
2
2 2
Þ m
n
e
v
n
r n ev r
n = ´ ´
´
= ´
1 1
2
1 1
2 2
Þ m
2
1 1
2
2
=
´ ev r
and m
1
1 1
2
1 = ´
ev r
Þ m
m
1
2
2
=
Hence magnetic moment decreases two
times correct option is (b).
3. For H-like atom E
n
n
=
- (13.6)Z eV
2
2
Here E
z
2
2
4
=
-(13.6)
 and E z
1
2
= - 13.6
E E
2 1
- = 40.8 eV
Þ 13.6 40.8 Z
2
1
1
4
´ -
é
ë
ê
ù
û
ú
=
Þ Z
2
408 4
13 6 3
=
´
´
Þ
.
.
 Z
2
4 =
Þ   Z = 2
Energy needed to remove the electron from
ground state is 
- = + ´ = + ´ = E Z
1
2
4 ( ) 13.6 13.6 54.4 eV
Hence correct option is (a).
i
e
T
e
r
u
ev
r
n
n
n
n
n
n
= = =
2
2
p
p
Q u
n
n
µ
1
 and r
n
n
µ
1
2
Þ i
n
n
µ
1
3
 Þ 
i
i
2
1
3
1
2
=
Þ i i
1 2
8 =
Hence current increases 8 times correct
option is (c).
5. Since five dark lines are pos si ble hence atom 
is ex cited to n = 6 state.
The number of transition in emission line 
=
- n n ( ) 1
2
Number of emission transition =
´
=
6 5
2
15
Hence correct option is (c).
6. A r
n n
= p
2
 for hydrozen atom r kn
n
=
2
where k is constant.
Þ A k n
n
= p
2 4
Þ A k
1
2
= p µ 
A
A
n
n
1
4
=
 75
Taking log both sides log log
A
A
n
n
1
4
æ
è
ç
ç
ö
ø
÷
÷
=
Hence it is a straight line with slope = 4
Correct option is (b)
7. For hydrogen atom i
n
n
µ
1
3
 and
  B
i
r
n
n
n
µ µ B k
n
n
=
1
5
[ ] Q r n
n
´
2
Þ B
k
2
5
2
= and B k
1
=
Þ 
B
B
2
1
5
1
2
1
32
= =
Þ B B
1 2
32 =
Hence magnatic field increases 32 times.
The correct option is (d).
8. For H-atom Lyman se ries is given by
1 1
1
1
2 2
l
= -
é
ë
ê
ù
û
ú
R
n
 for first line n = 2
Þ 
1
1
1
2
2
l
= -
é
ë
ê
ù
û
ú
R
Þ 
1 3
4 l
=
R
Momentum of photon P
h
p
=
l
Let momentum of atom p
A
Q Initial momentum was zero. Hence using
momentum conservation law, we get
p p
A B
= Þ Mv
h hR
= =
l
3
4
Þ     v
hR
M
=
3
4
Hence the correct option is (a).
9. Light wave equation is 
200 10
15 1
V/m 1.5 sec sin ( ) ´
-
t
´ ´
-
cos ( ) 0.5 sec 10
15 1
t
Here maximum frequency =
´ 1.5 10
2
15
p
Maxmum incident energy 
=
´
´
´
´
-
-
1.5 6.6
1.6
10
2
10
10
15 34
19
p
= 0.98 eV
Since work function = > 2eV maximum
energy hence no emission of electrons.
Thus correct option is (d).
10. Since in Balmer se ries of H-like atom
wave lengths (in  vis i ble re gion) are found
same or smaller hence the gas was ini tially
in sec ond ex cited state.
Cor rect op tion is (c).
11. For H-atom T n
H
= 2
3
p
and for H-like atom
T
n
z
x
=
2
3
2
p
For H-atom in ground state T
H
= 2p
For H-like atom in first excited state
   T
z z
x
=
´
=
´ ( ) 2 2 2 8
3
2 2
p p
But T T
H x
= 2 Þ 2
2 2 8
2
p
p
=
´ ´
z
Þ z
2
16 = 
Þ z = 4
Hence correct option is (c).
12. For K
a
 line of X-ray
1
1
2
2
l
= -
a
c
z ( )
Q z (atomic No.) for Pb Pb Pb
204 206 208
, ,
are same hence l l l
1 2 3
= = .
Hence correct option is (c).
13. The cor rect op tion is (d).
14. Since E
n
n
=
-13.6 eV
2
Þ E
1
= - 13.6 eV
and first excited state E
2
4
=
-13.6
eV
76
Þ                     E
2
= - 3.4 eV 
         DE E E = - =
2 1
10.2 if K < 10.2 eV
The electron collide elastically with H-atom 
in ground state.
The correct option is (c).
15. For Lyman se ries 
1 1
1
1
2 2
l
= -
é
ë
ê
ù
û
ú
R
n
 here n = 3
Þ 
1
1
1
9 l
= -
é
ë
ê
ù
û
ú
R 
Þ
1 8
9 l
=
R
P
h Rh
photon
= =
l
8
9
But P P
Photon H-atom
=
Þ 
8
9
Rh
M v
p
= ´
Þ v =
´ ´ ´ ´
´ ´ ´
-
-
8 10 10
9 10
7 34
31
1.097 6.6
1837 9.1
Þ v = 4 m/s
Hence correct option is (a).
16. Power = = ´ ´ ´ =
-
VI 150 10 10 10 1500
3 3
W
The 99% power heated the target hence
Heating power = ´ = ´
99
100
1500 15 99 W
The rate at which target is heated per sec.
(in cal)
   =
´
-
15 99
355
4.2
~
 Q1
1
J
4.2
cal =
é
ë
ê
ù
û
ú
Hence correct option is (c).
17. E
z
n
n
= -
´ 13.6 eV
2
2
E z
3
2
9
= -
13.6 eV
 and E z
4
2
16
=
-13.6 eV
DE E E z = - = ´ -
é
ë
ê
ù
û
ú
4 3
2
1
9
1
16
( ) 13.6 eV
Þ DE =
´ ´
´
=
13.6 eV)
32.4 eV
( 2 7
16 9
2
Þ z
2
9
7
49 =
´ ´
´
=
16 32.4
13.6
Þ z = 7
Hence correct option is (d).
18. l = = =
h
p
h
m K
h
m eV
p p
2 2
 
Þ 
10
10
2 1836 10 10
13
34
31 19
-
-
- -
=
´
´ ´ ´ ´ ´ ´
6.6
9.1 1.6 V
Þ V = ´ 8.15 volt 10
4
Hence correct option is (b).
19. Since E
n
n
µ
1
2
 and L n
n
µ
Hence E
L
n
n
µ
1
2
The correct option is (d).
20. Since m
p
n
n n
eu r
=
2
 Q u
n
n
µ
1
  and r n
n
µ
2
Þ m
n
kn =
Where k is constant for H-atom
For ground state m
1
1 = ´ = k k …(i)
For third excited state n = 4
m
2
4 4 = ´ = k k …(ii)
From Eqs. (i) and (ii) we get m m
2 1
4 =
Hence correct option is (d).
21. By con ser v a tion of mo men tum
M v M M v
H H H
= + ¢ ( ) Þ v
v
¢ =
2
Let initial KE of H-atom = K
Final KE of each-H-atom =
K
2
For excitation 
K
E E
2 4
2 1
= - =
-
+
13.6
13.6
Þ 
K
2
= 10.2 eV
Þ K = 20.4 eV
Hence correct option is (a).
 77
22. We know that for H-like atom
    E K
n n
= - Þ K
n
= 3.4 eV
l = =
h
p
h
m K
e
2
=
´
´ ´ ´ ´ ´
-
- -
6.6
9.1 3.4 1.6
10
2 10 10
34
31 19
Þ l = 6.6 Å
Hence both options (a) and (b) are correct.
Hence answer is (c) both are correct.
23-25. 0.6e
hc
W =
´
-
-
4950 10
10
 …(i)
1.1 e
hc
W = -
l
2
 …(ii)
Subtracting Eq. (i) from Eq. (ii) we get
0.5 e hc = -
´
é
ë
ê
ù
û
ú
-
1 1
4950 10
2
10
l
Þ 
0.5 1.6
6.62
´ ´
´ ´ ´
+
´
=
-
- -
10
10 3 10
1
4950 10
1
19
34 8 10
2
l
Þ l
2
~
- 4111 Å
From Eq. (i)
W =
´ ´ ´
´ ´ ´
-
-
- -
6.6
4.95 1.6
1.9 eV
10 3 10
10 10
34 8
7 19
~
23. W = 1.9 eV
Hence correct option is  (c).
24. l = 4111 Å 
Hence correct option is (c)
25. Since magnatic field does not change the KE
of elec trons hence re tard ing potential
re main same.
Hence correct option is (c).
26. ( )
max
KE eV eV eV = - = 5 3 2
= ´ ´ - 2 19 1.6 J
     l
min
= =
h
p
h
m K
e
2
Þ l
min
=
´
´ ´ ´ ´ ´
-
- -
6.6
2 9.1 1.6
10
10 2 10
34
31 19
= 8.69 Å
Hence correct option is (b).
27. Photo emis sion will stop when potential of
sphere be comes stop ping po ten tial
Þ 
1
4
2
0
p e
q
r
= V
Since ( )
max
KE eV =
0
hence V
0
2 =
Þ q r = 8
0
pe coulomb
Hence correct option is (b)
28. Let t be the time for photo emis sion 
1
4
2
0
pe
´ ´ =
q
r
t
t
r
q
=
8
0
pe
Intensity of light at 0.8 from source
I =
´
´
- ´
-
-
3.2
0.8
W/m
10
4
4 10
3
2
4 2
p ( )
~
Energy incident on the sphere in unit time
E
1
3 2 4 8
8 10 4 10 10 = ´ ´ ´ ´ = ´
- - -
p ( ) 8.04 W
Energy of each photon
E
2
19 19
5 10 8 10 = ´ ´ = ´
- -
1.6 J
Total number of photons incident on the
sphere per second
h = =
´
´
=
-
-
E
E
1
2
8
19
11
10
8 10
10
8.04
Since 10
6
 photons emit one electron.
Hence the total number of photoelectron
per sec is n
n
2
1
1
11
6
5
10
10
10
10 = = =
Therefore, 
q n e t t = ´ ´ = ´ ´ ´
-
2
5 19
10 10 1.6
Þ
9 10 10
2
9 14
´ ´ ´ ´
=
-
1.6 t
r
 
78
Page 5


¢ Objective Questions (Level 2)
1. F F
a c
= Þ 
GmM
r
mv
r
2
2
= …(i)
and mvr
nh
=
2p
 …(ii)
From Eq. (ii)
Þ v
nh
mr
=
2p
Putting this value in Eq. (i)
GM
r
h h
m r
=
2 2
2 2 2
4p
 
Þ r
n h
m GM
=
2 2
2 2
4 p
KE = =
´
=
1
2
1
2 2
2
mv
m GM
r
GMm
r
PE =
- GMm
r
Þ E = + KE PE
Þ E
GMm
r
GMm m GM
n h
=
-
=
- ´
2
4
2
2 2
2 2
p
Þ E
G M m
n h
=
-2
2 2 2 3
2 2
p
 for ground state n = 1
Þ E
G M m
n
=
- 2
2 2 2 3
2
p
Hence correct option is (b).
2. We have m p
n n n
n
n
i A
e
T
r = = ´
2
Þ m
p
p
n
n n
n
n n
e r u
r
eu r
=
´ ´ ´
=
2
2 2
Þ m
n
e
v
n
r n ev r
n = ´ ´
´
= ´
1 1
2
1 1
2 2
Þ m
2
1 1
2
2
=
´ ev r
and m
1
1 1
2
1 = ´
ev r
Þ m
m
1
2
2
=
Hence magnetic moment decreases two
times correct option is (b).
3. For H-like atom E
n
n
=
- (13.6)Z eV
2
2
Here E
z
2
2
4
=
-(13.6)
 and E z
1
2
= - 13.6
E E
2 1
- = 40.8 eV
Þ 13.6 40.8 Z
2
1
1
4
´ -
é
ë
ê
ù
û
ú
=
Þ Z
2
408 4
13 6 3
=
´
´
Þ
.
.
 Z
2
4 =
Þ   Z = 2
Energy needed to remove the electron from
ground state is 
- = + ´ = + ´ = E Z
1
2
4 ( ) 13.6 13.6 54.4 eV
Hence correct option is (a).
i
e
T
e
r
u
ev
r
n
n
n
n
n
n
= = =
2
2
p
p
Q u
n
n
µ
1
 and r
n
n
µ
1
2
Þ i
n
n
µ
1
3
 Þ 
i
i
2
1
3
1
2
=
Þ i i
1 2
8 =
Hence current increases 8 times correct
option is (c).
5. Since five dark lines are pos si ble hence atom 
is ex cited to n = 6 state.
The number of transition in emission line 
=
- n n ( ) 1
2
Number of emission transition =
´
=
6 5
2
15
Hence correct option is (c).
6. A r
n n
= p
2
 for hydrozen atom r kn
n
=
2
where k is constant.
Þ A k n
n
= p
2 4
Þ A k
1
2
= p µ 
A
A
n
n
1
4
=
 75
Taking log both sides log log
A
A
n
n
1
4
æ
è
ç
ç
ö
ø
÷
÷
=
Hence it is a straight line with slope = 4
Correct option is (b)
7. For hydrogen atom i
n
n
µ
1
3
 and
  B
i
r
n
n
n
µ µ B k
n
n
=
1
5
[ ] Q r n
n
´
2
Þ B
k
2
5
2
= and B k
1
=
Þ 
B
B
2
1
5
1
2
1
32
= =
Þ B B
1 2
32 =
Hence magnatic field increases 32 times.
The correct option is (d).
8. For H-atom Lyman se ries is given by
1 1
1
1
2 2
l
= -
é
ë
ê
ù
û
ú
R
n
 for first line n = 2
Þ 
1
1
1
2
2
l
= -
é
ë
ê
ù
û
ú
R
Þ 
1 3
4 l
=
R
Momentum of photon P
h
p
=
l
Let momentum of atom p
A
Q Initial momentum was zero. Hence using
momentum conservation law, we get
p p
A B
= Þ Mv
h hR
= =
l
3
4
Þ     v
hR
M
=
3
4
Hence the correct option is (a).
9. Light wave equation is 
200 10
15 1
V/m 1.5 sec sin ( ) ´
-
t
´ ´
-
cos ( ) 0.5 sec 10
15 1
t
Here maximum frequency =
´ 1.5 10
2
15
p
Maxmum incident energy 
=
´
´
´
´
-
-
1.5 6.6
1.6
10
2
10
10
15 34
19
p
= 0.98 eV
Since work function = > 2eV maximum
energy hence no emission of electrons.
Thus correct option is (d).
10. Since in Balmer se ries of H-like atom
wave lengths (in  vis i ble re gion) are found
same or smaller hence the gas was ini tially
in sec ond ex cited state.
Cor rect op tion is (c).
11. For H-atom T n
H
= 2
3
p
and for H-like atom
T
n
z
x
=
2
3
2
p
For H-atom in ground state T
H
= 2p
For H-like atom in first excited state
   T
z z
x
=
´
=
´ ( ) 2 2 2 8
3
2 2
p p
But T T
H x
= 2 Þ 2
2 2 8
2
p
p
=
´ ´
z
Þ z
2
16 = 
Þ z = 4
Hence correct option is (c).
12. For K
a
 line of X-ray
1
1
2
2
l
= -
a
c
z ( )
Q z (atomic No.) for Pb Pb Pb
204 206 208
, ,
are same hence l l l
1 2 3
= = .
Hence correct option is (c).
13. The cor rect op tion is (d).
14. Since E
n
n
=
-13.6 eV
2
Þ E
1
= - 13.6 eV
and first excited state E
2
4
=
-13.6
eV
76
Þ                     E
2
= - 3.4 eV 
         DE E E = - =
2 1
10.2 if K < 10.2 eV
The electron collide elastically with H-atom 
in ground state.
The correct option is (c).
15. For Lyman se ries 
1 1
1
1
2 2
l
= -
é
ë
ê
ù
û
ú
R
n
 here n = 3
Þ 
1
1
1
9 l
= -
é
ë
ê
ù
û
ú
R 
Þ
1 8
9 l
=
R
P
h Rh
photon
= =
l
8
9
But P P
Photon H-atom
=
Þ 
8
9
Rh
M v
p
= ´
Þ v =
´ ´ ´ ´
´ ´ ´
-
-
8 10 10
9 10
7 34
31
1.097 6.6
1837 9.1
Þ v = 4 m/s
Hence correct option is (a).
16. Power = = ´ ´ ´ =
-
VI 150 10 10 10 1500
3 3
W
The 99% power heated the target hence
Heating power = ´ = ´
99
100
1500 15 99 W
The rate at which target is heated per sec.
(in cal)
   =
´
-
15 99
355
4.2
~
 Q1
1
J
4.2
cal =
é
ë
ê
ù
û
ú
Hence correct option is (c).
17. E
z
n
n
= -
´ 13.6 eV
2
2
E z
3
2
9
= -
13.6 eV
 and E z
4
2
16
=
-13.6 eV
DE E E z = - = ´ -
é
ë
ê
ù
û
ú
4 3
2
1
9
1
16
( ) 13.6 eV
Þ DE =
´ ´
´
=
13.6 eV)
32.4 eV
( 2 7
16 9
2
Þ z
2
9
7
49 =
´ ´
´
=
16 32.4
13.6
Þ z = 7
Hence correct option is (d).
18. l = = =
h
p
h
m K
h
m eV
p p
2 2
 
Þ 
10
10
2 1836 10 10
13
34
31 19
-
-
- -
=
´
´ ´ ´ ´ ´ ´
6.6
9.1 1.6 V
Þ V = ´ 8.15 volt 10
4
Hence correct option is (b).
19. Since E
n
n
µ
1
2
 and L n
n
µ
Hence E
L
n
n
µ
1
2
The correct option is (d).
20. Since m
p
n
n n
eu r
=
2
 Q u
n
n
µ
1
  and r n
n
µ
2
Þ m
n
kn =
Where k is constant for H-atom
For ground state m
1
1 = ´ = k k …(i)
For third excited state n = 4
m
2
4 4 = ´ = k k …(ii)
From Eqs. (i) and (ii) we get m m
2 1
4 =
Hence correct option is (d).
21. By con ser v a tion of mo men tum
M v M M v
H H H
= + ¢ ( ) Þ v
v
¢ =
2
Let initial KE of H-atom = K
Final KE of each-H-atom =
K
2
For excitation 
K
E E
2 4
2 1
= - =
-
+
13.6
13.6
Þ 
K
2
= 10.2 eV
Þ K = 20.4 eV
Hence correct option is (a).
 77
22. We know that for H-like atom
    E K
n n
= - Þ K
n
= 3.4 eV
l = =
h
p
h
m K
e
2
=
´
´ ´ ´ ´ ´
-
- -
6.6
9.1 3.4 1.6
10
2 10 10
34
31 19
Þ l = 6.6 Å
Hence both options (a) and (b) are correct.
Hence answer is (c) both are correct.
23-25. 0.6e
hc
W =
´
-
-
4950 10
10
 …(i)
1.1 e
hc
W = -
l
2
 …(ii)
Subtracting Eq. (i) from Eq. (ii) we get
0.5 e hc = -
´
é
ë
ê
ù
û
ú
-
1 1
4950 10
2
10
l
Þ 
0.5 1.6
6.62
´ ´
´ ´ ´
+
´
=
-
- -
10
10 3 10
1
4950 10
1
19
34 8 10
2
l
Þ l
2
~
- 4111 Å
From Eq. (i)
W =
´ ´ ´
´ ´ ´
-
-
- -
6.6
4.95 1.6
1.9 eV
10 3 10
10 10
34 8
7 19
~
23. W = 1.9 eV
Hence correct option is  (c).
24. l = 4111 Å 
Hence correct option is (c)
25. Since magnatic field does not change the KE
of elec trons hence re tard ing potential
re main same.
Hence correct option is (c).
26. ( )
max
KE eV eV eV = - = 5 3 2
= ´ ´ - 2 19 1.6 J
     l
min
= =
h
p
h
m K
e
2
Þ l
min
=
´
´ ´ ´ ´ ´
-
- -
6.6
2 9.1 1.6
10
10 2 10
34
31 19
= 8.69 Å
Hence correct option is (b).
27. Photo emis sion will stop when potential of
sphere be comes stop ping po ten tial
Þ 
1
4
2
0
p e
q
r
= V
Since ( )
max
KE eV =
0
hence V
0
2 =
Þ q r = 8
0
pe coulomb
Hence correct option is (b)
28. Let t be the time for photo emis sion 
1
4
2
0
pe
´ ´ =
q
r
t
t
r
q
=
8
0
pe
Intensity of light at 0.8 from source
I =
´
´
- ´
-
-
3.2
0.8
W/m
10
4
4 10
3
2
4 2
p ( )
~
Energy incident on the sphere in unit time
E
1
3 2 4 8
8 10 4 10 10 = ´ ´ ´ ´ = ´
- - -
p ( ) 8.04 W
Energy of each photon
E
2
19 19
5 10 8 10 = ´ ´ = ´
- -
1.6 J
Total number of photons incident on the
sphere per second
h = =
´
´
=
-
-
E
E
1
2
8
19
11
10
8 10
10
8.04
Since 10
6
 photons emit one electron.
Hence the total number of photoelectron
per sec is n
n
2
1
1
11
6
5
10
10
10
10 = = =
Therefore, 
q n e t t = ´ ´ = ´ ´ ´
-
2
5 19
10 10 1.6
Þ
9 10 10
2
9 14
´ ´ ´ ´
=
-
1.6 t
r
 
78
t =
´ ´
´ ´
-
-
2 8 10
9 10
3
5
1.6
 Þ t = 111 s
Hence correct option is (c).
¢ More than one op tions are cor rect
1. Since l
0
=
hc
eV
 if v in creases l
0
 de creases
hence the in ter val be tween l
a K
 and l
0
 as
well as l
b K
 and l
0
 in creases.
The correct options are  (b) and (c).
2. R n µ
2
, V
n
µ
1
 and E
n
µ
1
2
 for Bohr model of
H-atom
Þ VR n µ and 
V
E
n µ
Hence, the correct options are (a) and (c).
3. For Bohr model of H-atom
L n µ ,    r n µ
2
  and   T n µ
3
 
Hence 
rL
T
 is independent of n
L
T n
µ
1
2
 and 
T
r
n L n µ µ ,
3
Hence correct options are (a), (b) and (c).
4. Q l =
h
mv
 and l =
h
mK 2
Hence heavy particle has smallest
wavelength when speed and KE both
particle are same.
The correct options are (a) and (c).
5. Since there are six different wave length
Hence, final state will be n = 4.
Since two wavelengths are longer than l
0
 
[(From n = ® 4 3 and n = ® 3 2)]
Hence initial state was n = 2
and there are three transitions shown as
(1), (2) and (3) belonging to Lymen series.
Hence correct options are (a), (b) and (d).
6. Q f a z b = - ( )
f versus z is a straight line
Q f
c
=
l
 Þ 
1
l
= -
a
c
z b ( )
hence
1
l
  versus z is a straight line
f a z b = -
2
( )
Þ log log log ( ) f a z b = + -
2
 which is a
straight line
Hence correct options are (a), (b) and (c).
¢ Match the Columns :
1. Lymen se ries lies in UV re gion, Balmer
se ries lies in vis i ble re gion and Paschen and
Brackelt se ries lie in infrared re gion. Hence
(a) r
(b) q
(c) p
(d) p
 2. For H-atom E
n
n
=
-13.6
eV
2
Þ    E
2
2
2
=
-13.6
eV =
-13.6
eV
4
Ionization energy from first excited state of 
H-atom
E E = - =
2
4
13.6
eV …(i)
For He
+
 ion
E
n
Z
H (
( )
He)
13.6 eV
=
-
´
2
2
 for He
+
= z 2
Þ E
n
( ) He =
-
´
13.6 eV
n
2
4
Ionization energy of He
+
 atom from ground
state = ´ = ´ ( ) 13.6 eV 4 4 4 E from Eq. (i)
    = 16 E
 79
n = 4
n = 3
n = 2
n = 1
1
2 3