Page # 54 MODERN PHYSICS

Exercise - V (JEE-PROBLEMS)
4. The transition from the state n = 4 to n = 3 in
1. (a) Imagine an atom made up of a proton
a hydrogen like atom results in ultraviolet radiation.
and a hypothetical particle of double the mass of
Infrared radiation will be obtained in the transition
the electron but having the same charge as the
[JEE 2001]
electron. Apply the Bohr atom model and consider
(A) 2  1 (B) 3  2
all possible transitions of this hypothetical particle
(C) 4  2 (D) 5  4
to the first excited level. The longest wavelength
photon that will be emitted has wavelenght  5. The intensity of X-rays from a coolidge tube
(given in terms of the Rydberg constant R for the is plotted agianst wavelength  as shown in the
hydrogen atom) equal to [JEE’2000(Scr)] figure. The minimum wavelength found is c and
(A) 9/(5R) (B) 36/(5R) the wavelength of K line is k. As the accelerating
(C) 18/(5R) (D) 4/R voltage is increased. [JEE 2001]
(b) The electron in a hydrogen atom makes a l
transition from an excited state to the ground
state. Which of the following statements is true
? [JEE’2000(Scr)]
(A) Its kinetic energy increases and its potential
and total energies decrease (A) k – c increases (B) k – c decreases
(B) Its kinetic energy decreases, potential energy (C) k increases (D) k decreases
increases and its total energy remains the same
6. The potential difference applied to an X-ray
(C) Its kinetic and total energies decrease and
tube is 5kV and the current through it is 3.2 mA.
its potential energy increases
Then the number of electrons striking the target
(D) Its kinetic, potential and total energies
per second is [JEE’2002(Scr)]
decrease
(A) 2 × 1016 (B) 5 × 1016
2. (a) A hydrogen-like atom of atomic number Z (C) 1 × 1017 (D) 4 × 1015
is in an excited state of quantum number 2n. It
7. A Hydrogen atom and Li++ion are both in the
can emit a maximum energy photon of 204eV. If
second excited state. If l H and l Li are their
it makes a transition to quantum state n, a photon
respective electronic angular momenta, and EH
of energy 40.8 eV is emitted. Find n, Z and the
and ELi their respective energies, then
ground state energy (in eV) for this atom. Also,
[JEE’2002(Scr)]
calculate the minimum energy (in eV) that can
(A) lH > lLi and |EH| > |ELi|
be emitted by this atom during de-excitation.
(B) lH = lLi and |EH| < |ELi|
Ground state energy of hydrogen atom is
(C) lH = lLi and |EH| > |ELi|
–13.6 eV. [JEE’2000]
(D) lH < lLi and |EH| < |ELi|
(b) When a beam of 10.6 eV photon of intensity
8. A hydrogen like atom (described by the Bohr
2W/m2 falls on a platinum surface of area 1 ×
model) is observed to emit six wavelengths,
104m2 and work function 5.6 eV, 0.53% of the
originating from all possible transition between a
incident photons eject photoelectrons. Find the
group of levels. These levels have energies
number of photoelectron emitted per sec and their
between –0.85 eV and –0.544 eV (including both
minimum and maximum energies in eV.
these values)
[JEE’2000]
(a) Find the atomic number of the atom.
3. Electrons with energy 80 keV are incident on
(b) Calculate the smallest wavelength emitted in
the tungsten target of an X-ray tube. K-shell
these transitions. [JEE’2002]
electrons of tungsten have 72.5 keV energy. X-
rays emitted by the tube contain only 9. Two metallic plates A and B each of area 5 ×
(A) a continuous X-ray spectrum (Bremsstrahlung) 10–4 m2, are placed at a separation of 1cm. Plate
with a minimum wavelength of  0.115 Å B carries a positive charge of 33.7 × 10–12 C. A
(B) a continuous X-ray spectrum (Bremsstrahlung) monochromatic beam of light, with photons of
with all wavelengths energy 5 eV each, starts falling on plate A at t =
(C) the characteristic X-ray spectrum of tungsten 0 so that 1016 photon fall on it per square meter
(D)a continous X-ray spectrum(Bremmstrahlung) per second. Assume that one photoelectron is
with a minimum wavelength of  0.155 Å and the emitted for every 106 incident photons. Also
characteristic X-ray spectrum of tangtsen assume that all the emitted photoelectrons are
[JEE 2000] collected by plate B and the work function of

394,50 - Rajeev Gandhi Nagar Kota, Ph. No. : 93141-87482, 0744-2209671

IVRS No : 0744-2439051, 52, 53, www. motioniitjee.com, info@motioniitjee.com
 MODERN PHYSICS Page # 55

plate A remains constant at the value 2 eV. (C) A and B will have different intensities while A
Determine and C will have equal frequencies.
(a) the number of photoelectrons emitted up to (D) A and B will have equal intensities while B
t = 10 sec. and C will have different frequencies.
(b) the magnitude of the electric field between 15.A proton has kinetic energy E = 100 keV which
the plates A and B at t = 10 s and is eqal to that of a photon. The wavelength of
(c) the kinetic energy of the most energetic photon is 2 and that of proton is 1. The ratio of
photoelectron emitted at t = 10 s when it reaches 2/1 is proportional to [JEE 2004 (Scr.)]
1
plate B. 
2
(Neglect the time taken by photoelectron to reach (A) E2 (B) E
1
plate B) [JEE’2002] (C) E–1 (D) E 2
10.If the atom 100Fm257 follows Bohr model and
the radius of last orbit of 100Fm257 is n times the 16 In a photoelectric setup, the radiations from
Bohr radius, then find n the Balmer series of hydrogen atom are incident
[JEE 2003] on a metal surface of work function 2eV. The
(A) 100 (B) 200 wavelength of incident radiations lies between
450 nm to 700 nm. Find the maximum kinetic
1 energy of photoelectron emitted. (Given hc/e =
(C) 4 (D)
4 1242 eV-nm). [JEE 2004]
11.The attractive potential for an atom is given 17.The wavelength of K X – ray of an element
by v = v0 ln (r/r0), v0 and r0 are constant and r is having atomic number z = 11 is . The wavelength
the radius of the orbit. The radius r of the nth of K X-ray of another element of atomic number
Bohr’s orbit depends upon principal quantum z is 4l. Then z is [JEE’ 2005 (Scr)]
number n as : [JEE’2003(Scr)] (A) 11 (B) 44
(A) r  n (B) r  1/n2 (C) 6 (D) 4
(C) r  n2 (D) r  1/n
18.A photon of 10.2 eV energy collides with a
12. Frequency of a photon emitted due to hydrogen atom in ground state inelastically. After
transition of electron of certain elemrnt from L to few microseconds one more photon of energy 15
K shell is found to be 4.2 × 1018 Hz. Using eV collides with the same hydrogen atom. Then
Moseley’s law, find the atomic number of the what can be detected by a suitable detector.
element, given that the Rydberg’s constant (A) one photon of 10.2 eV and an electron of
R = 1.1 × 107 m–1. [JEE’2003] energy 1.4 eV
13.In a photoelctric experiment set up, photons (B) 2 photons of energy 10.2 eV
of energy 5 eV falls on the cathode having work (C) 2 photons of energy 3.4 eV
function 3eV. (D) 1 photon of 3.4 eV and one electron of 1.4
(a) If the saturation current is iA = 4A for eV [JEE’ 2005 (Scr)]
intensity 10–5 W/m2, then plot a graph between 19.In Young’s double slit experiment an electron
anode potential and current. beam is used to form a fringe pattern instead of
(b) Also draw a graph for intensity of incident light. If speed of the electrons is increased then
radiation of 2 × 10–5 W/m2 ? [JEE’2003] the fringe width will :
(A) increase (B) decrease
14.In a photoelectric experiment anode potential (C) remains same
is plotted against plate current[JEE 2004 (Scr.)] (D) no fringe pattern will be formed
I
20.The potential energy of a particle of mass m
is given by
B E0 0  x  1
C
A V(x) =  
0 x1 
1 and 2 are the de-Broglie wavelengths of the
V particle, when 0 x  1 and x > 1 respectively. If
the total energy of particle is 2E0, find 1/2
(A) A and B will have different intensities while B [JEE 2005]
and C will have different frequencies.
21.Highly energetic electrons are bombarded on
(B) B and C will have different intensities while A
a target of an element containing 30 neutrons.
and C will have different frequencies.
The ratio of radii of nucleus to that of helium

394,50 - Rajeev Gandhi Nagar Kota, Ph. No. : 93141-87482, 0744-2209671

IVRS No : 0744-2439051, 52, 53, www. motioniitjee.com, info@motioniitjee.com
 Page # 56 MODERN PHYSICS
nucleus is (14)1/3. Find
(a) atomic number of the nucleus 26.The largest wavelength in the ultraviolet
(b) the frequency of K line of the X-ray produced. region of the hydrogen spectrum is 122 nm. The
(R = 1.1 × 107 m–1 and c = 3 × 108 m/s) smallest wavelength in the infrared region of the
[JEE 2005] hydrogen spectrum (to the nearest integer) is :
(A) 802 nm (B) 823 nm [JEE 2007]
22.The graph between 1/ and stopping potential
(C) 1882 nm (D) 1648 nm
(V) of three metals having work functions 1, 2
and 3 in an experiment of photoelectric effect is 27.Which one of the following statements is
plotted as shown in the figure. Which of the WRONG in the context of X-rays generated from
following statement(s) is/are correct? [Here a X-ray tube?
 is the wavelength of incident ray]. (A) Wavele ngth of characteris tic X-rays
metal 1 metal 2 metal 3 decreases when the atomic number of the target
V increases.
(B) Cut-off wavelength of the continuous X-rays
depends on the atomic number of the target.
 (C) Intensity of the characteristic X-rays depends
on the electrical power given to the X-ray tube
0.001 0.002 0.004 1/ nm–1
(D) Cut-off wavelength of the continuous X-rays
(A) Ratio of work functions 1 : 2 : 3 = 1 : 2 : 4 depends on the energy of the electrons in the X-
(B) Ratio of work functions 1 : 2 : 3= 4 : 2 : 1 rays tube [JEE 2008]
(C) tan  is directly proportional to hc/e, where
h is Planck’s constant and c is the speed of light Paragraph for Question No. 28 to 30
(D) The vio let colo ur light can eje ct In mixture of H–He+ gas (He+ is singly ionized
photoelectrons from metals 2 and 3.[JEE 2006] He atom), H atoms and He+ ions are excited to
their respective first excited states.
23.In hydrogen-like atom (z = 11), nth line of Subsequently, H atoms transfer their total
Lyman series has wavelength  equal to the de- excitation energy to He– ions (by collision).
Broglie’s wavelength of electron in the level from Assume that the Bohr model of atom is exactly
which it originated. What is the value of n? valid.
[Take : Bohr radius (r0) = 0.53 Å and Rydberg [JEE 2008]
constant (R) = 1.1 × 107 m–1] [JEE 2006] 28.The quantum number n of the state finally
24.STATEMENT-1 poulated in He+ ions is
(A) 2 (B) 3
If the accelerating potential in an X-ray tube is
(C) 4 (D) 5
increased, the wavelengths of the characteristic
X-rays do not change. [JEE 2007] 29.The wavelength of light emitted in the
visible region by He+ ions after collisions with H
because
atoms is
STATEMENT-2
(A) 6.5 × 10–7 m (B) 5.6 × 10–7m
–7
When an electron beam strikes the target in an (C) 4.8 × 10 m (D) 4.0 × 10–7m
X-ray tube, part of the kinetic energy is converted
30.The ratio of the kinetic energy of the n = 2
into X-ray energy.
electron for the H atom to that of He+ ion is
(A) Statement-1 is True, Statement-2 is True;
Statement-2 is a correct explanation for 1 1
(A) (B)
Statement-1 4 2
(B) Statement-1 is True, Statement-2 is True; (C) 1 (D) 2
Statement-2 is NOT a correct explanation for
Statement-1 Paragraph for Questions 31 to 33
(C) Statement-1 is True, Statement-2 is False When a particle is restricted to move along x-
(D) Statement-1 is False, Statement-2 is True axis between x = 0 and x = a, where a is of
nanometer dimension, its energy can take only
25.Electrons with de-Broglie wavelength  fall on certain specific values. The allowed energies of
the target in an X-ray tube. The cut-off the particle moving in such a restricted region,
wavelength of the emitted X-rays is[JEE 2007] correspond to the formation of standing waves
with nodes at its ends x = 0 and x = a. The
2mc2 2h
(A)  0  (B)  0  wavelength of this standing wave is related to
h mc the linear momentum p of the particle according
2m 2 c 2 3 to the de Broglie relation. The energy of the
(C)  0  (D) 0 =  particle of mass m is related to its linear
h2

394,50 - Rajeev Gandhi Nagar Kota, Ph. No. : 93141-87482, 0744-2209671

IVRS No : 0744-2439051, 52, 53, www. motioniitjee.com, info@motioniitjee.com
 MODERN PHYSICS Page # 57
p2
momentum as E = . Thus, the energy of the 36.A diatomic molecule has moment of inertia I.
2m By Bohr's quantization condition its rotational
particle can be denoted by a quantum number ‘n’
taking values 1, 2, 3 … (n = 1, called the ground energy in the nth level (n = 0 is not allowed ) is
state) corresponding to the number of loops in
the standing wave. Use the model described above 1  h2  1  h2 
to answer the following three questions for a (A)  2  (B) n  2 
n2  8 I 
   8 I 
particle moving in the line x = 0 to x = a.Take h =
6.6 × 10–34 Jsand e= 1.6 × 10–19 C. [JEE 2009]
 h2  2 h
2

31.The allowed energy for the particle for a (C) n 2  (D) n  2 
particular value of n is proportional to  8 I   8 I 
(A) a–2 (B) a–3/2 37.It is found that the excitation frequency from
–1
(C) a (D) a2 ground to the first excited state of rotation for
32.If the mass of the particle is m = 1.0 × 10–30 4 11
kg and a = 6.6 nm, the energy of the particle in the CO molecule is close to  10 Hz. Then the

its ground state is closest to moment of inertia of CO molecule about its center
(A) 0.8 meV (B) 8 meV of mass is close to (Take h = 2 × 10–34 Js)
(C) 80 meV (D) 800 meV (A) 2.76 × 10–46 kg m2
33.The speed of the particle, that can take (B) 1.87 × 10–46 kg m2
discrete values, is proportional to (C) 4.67 × 10–47 kg m2
(A) n –3/2 (B) n –1 (D) 1.17 × 10–47 kg m2
1/2
(C) n (D) n 38.In a CO molecule, the distance between C
34.Photoelectric effect experiments are (mass = 12 a.m.u.) and O (mass = 16 a.m.u.)
5 – 27
performed using three different metal plates p, q where 1 a.m.u. =  10 kg, is close to
and r having work functions p = 2.0 eV, q = 2.5 3
–10
(A) 2.4 × 10 m (B) 1.9 × 10–10 m
eV and r = 3.0 eV, respectively. A light beam –10
(C) 1.3 × 10 m (D) 4.4 × 10–11 m
containing wavelengths of 550 nm, 450 nm and
350 nm with equal intensities illuminates each of 39.The wavelength of the first spectral line in
o
the plates. The correct I–V graph for the the Balmer series of hydrogen atom is 6561 A .
experiment is [JEE 2009] The wavelength of the second spectral line in
I
I the Balmer series of singly-ionized helium atom is
[JEE-2011]
p
q o o
(A) (B) r
(A) 1215 A (B) 1640 A
o o
V V (C) 2430 A (D) 4687 A
I
I 40.A silver sphere of radius 1 cm and work func-
r
q
tion 4.7 eV is suspended from an insulating thread
(C) p (D) r in free-space. It is under continuous illumination
p
q of 200 nm wavelength light. As photoelectrons
V are emitted, the sphere gets charged and ac-
35.An  - particle and a proton are accelerated quires a potential. The maximum number of pho-
from rest by a potential difference of 100 V. After toelectrons emitted from the sphere is A × 10z (
this, their de Broglie wavelengths are a and p
p where 1 < A < 10). The value of 'Z' is
respectively. The ratio , to the nearst integer,, [JEE-2011]

is [JEE 2010] 41.A proton is fired from very far away towards
Paragraph for questions 36 to 38 a nucleus with charge Q = 120 e, where e is the
The key feature of Bohr's theory of spectrum of electronic charge. It makes a closest approach
hydrogen atoms is the quantization of angular of 10 fm to the nucleus. The de Broglie wave-
momentum when an electron is revolving around length (in units of fm) of the proton at its start
a proton. We will extend this to a general -27
is: (take the proton mass, mp = (5/3) x 10 kg;
rotational motion to find quantized rotational
energy of a diatomic molecule assuming it to be -15 1 9
rigid. The rule to be applied is Bohr's quantization h/e = 4.2 x 10 J.s/C; = 9 X 10 m/F; 1 fm
4 o
condition. [JEE 2010]

394,50 - Rajeev Gandhi Nagar Kota, Ph. No. : 93141-87482, 0744-2209671

IVRS No : 0744-2439051, 52, 53, www. motioniitjee.com, info@motioniitjee.com