dpps_3atomic_structure-1__03-6-14

8/11/2019 DPPS___3__Atomic_Structure-1__03-6-14

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CAREER POINT

PRACTICE PROBLEM SHEET

PHYSICS

Topic Atomic Structure-3

Question based on Spectrum and spectrum lines

Q.1 If the series limit wavelength of the Lyman series for hydrogen atom is 912 , then the series limitwavelength for the Balmer series for the hydrogen atom is -

(1) 912 (2) 912 2 (3) 912 ()2

912

Q.2 In hydrogen s!e"tr#m, the shortest wavelength in Balmer series is $ %he shortest wavelength in Bra"&ett

series will 'e -

(1) 2 (2) (3) 9 () 1

Q.3 If the wave n#m'er of a s!e"tral line of Bra"&ett series of hydrogen is))

9times the *yd'erg "onstant$

+hat is the state from whi"h the transition has ta&en !la"e

(1) n (2) n . (3) n () n /

Q.4 0or the first mem'er of Balmer series of -s!e"tr#m, the wavelength is $ +hat is the wavelength of these"ond mem'er

(1) 3)

.

(2) 1(

3

(3) 9

() 2/

2

Q.5 If 1 and 2 are the wavelengths of the first mem'ers of the Lyman and as"hen series res!e"tively, then 12is 4(1) 13 (2) 13 (3) /. () /15

Q.6 6le"trons in a "ertain energy level n n 1, "an emit 3 s!e"tral lines$ +hen they are in another energy level,n n2$ %hey "an emit s!e"tral lines$ %he s!eed of the ele"trons in the two or'its are in the ratio4(1) 3 (2) 3 (3) 2 1 () 1 2

Q.7 0or an atom of ion having single ele"tron, the following wavelengths are o'served$ +hat is the val#e ofmissing wavelength, x

(1) 2 mm (2) mm (3) mm () 12 mm

Q.8 %he a""eleration of ele"tron in the first or'it of hydrogen atom is4

(1)3

2

h

m(2)

mr

h

2

2

(3)

322

2

rm

h

()

32

22

r

hm

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Q.! 8 !arti"le of mass m moves aro#nd in a "ir"#lar or'it in a "entro symmetri" !otential field ( )2

2Kr

ru = $

sing Bohr:s ;#anti


3/4

mmR

11912

19/5

===

912

2. ,2

=

22

21

111

nnR

0or shortest wavelength in Balmer series$

n1 2, n2

=

1

11R or

R

=

=

221

1

:

1R F ===

1:

RR

3.,2 1

*

9 *

22

14

1

n

4. ,4 1

*

223

14

2

13(

.R

:

1

*

22

1421

1(12R F

:

3(.R

R12

1(

5. ,4 0or Lyman series, n1 1 and n2 2 for firstline

3

1

1

1

2

1

1

1122

1

RRR =

=

=

0or as"hen series n1 3 and n2 for firstline

1

/

1

1

9

1

1

3

11

222

RRR =

=

=

15

/

/?1

3?

2

1 ==

R

R

6. ,1 =#m'er of emission s!e"tral lines

2

)1( =

nnN

2

)1(3 11

=

nn (in first

"ase)

or 121 =nn or (n14 3) (n1G 2)

%a&e !ositive root n1 3

8gain, 2

)1(

22 =

nn

(in se"ond "ase)

or 12222 = nn or (n24 ) (n2G 3)

%a&e !ositive root, or n2 =ow, velo"ity of ele"tron

nh

KZev

22=

3

1

2

1

1==

n

n

v

v

7. ,4 0rom *its "om'ination !rin"i!le

122313

111

nnnnnn +

=

Hr

11

1+=

x or x 12 mm

8. ,3

!. ,1r

mvKrru

dr

dF

2

)( ===

or mKrmv 2= and mvr 2nh

=2

2 nhmkrr or

2

1

=Km

nhr

and

mv2 Kr2

Km

nhK

%6 6 G 6

m

Knh

Km

nhK

Km

nhK

=

+

2221

1.,3 m$v$ c

E

=22 1

1

.

1$13E

2$1 1415J

v 52/

15

131/$1

11$2

=

mc

EF v $19

m?s

11.,1 1 red'#rg 13$ eK o, the energy needed to deta"h the ele"tron

is 13$ eK$%he energy in the gro#nd state

1 4 13$eK%he energy in first eA"ited state

2

1 4 13$ eK

5$

122=

= hc

3

12.,1 D i8 r

ev

2 r2 ef r2

13.,3 8!!ly "on"e!t of red#"ed mass

= emar F em2

2

ar =

14.,4 mto 'e re!la"ed 'y red#"ed mass s#"h that

mM

111+=

15.,3 0or "entre of mass at Oele"tron at Aand n#"le#satB, the !osition of "entre of mass OfromAis

CAREER POINT, CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 0744-3040000 3


4/4

mM

Mr

mM

rMomr

+=

++

=1

16.,2 r3 r1 n2x 32 9x 2r n,

x

x

n

r

=

=

= 3922

CAREER POINT, CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 0744-3040000

dpps___3__atomic_structure-1__03-6-14

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dpps_3atomic_structure-1__03-6-14