Chapter 14 Dual Nature of Radiation and Matter
1. Choose the correct answer.
i) A photocell is used to automatically switch on the
street lights in the evening when the sunlight is low in intensity. Thus it has
to work with visible light. The material of the cathode of the photocell is
(A) zinc
(B) aluminum
(C) nickel
(D) potassium
Answer:
(D) potassium
ii) Polychromatic (containing many different frequencies)
radiation is used in an experiment on the photoelectric effect. The stopping
potential
(A) will depend on the average wavelength
(B) will depend on the longest wavelength
(C) will depend on the shortest wavelength
(D) does not depend on the wavelength
Answer:
(C) will depend on the shortest wavelength
iii) An electron, a proton, an α-particle and a hydrogen
atom are moving with the same kinetic energy. The associated de Broglie
wavelength will be longest for
(A) electron
(B) proton
(C) α-particle
(D) hydrogen atom
Answer:
(A) electron
v) The equation E = pc is valid
(A) for all sub-atomic particles
(B) is valid for an electron but not for a photon
(C) is valid for a photon but not for an electron
(D) is valid for both an electron and a photon
Answer:
(C) is valid for a photon but not for an electron
2. Answer in brief.
i) What is photoelectric effect?
Answer:
The phenomenon of emission of electrons from a metal surface when
electromagnetic radiation of appropriate frequency is incident on it is known
as photoelectric effect.
ii) Can microwaves be used in the experiment on
photoelectric effect?
Answer:
No
iii) Is it always possible to see photoelectric effect
with red light?
Answer:
No
iv) Using the values of work function given in Table
14.1, tell which metal will require the highest frequency of incident radiation
to generate photocurrent.
Answer:
Gold.
[ Note : W0 = hv0, where h is Planck’s constant. The
larger the work function (W0), the higher is the threshold frequency
(v0). ]
v) What do you understand by the term wave-particle
duality? Where does it apply?
Answer:
Depending upon experimental conditions or structure of matter, electromagnetic
radiation and material particles exhibit wave nature or particle nature. This
is known as wave-particle duality.
It applies to all phenomena. The wave nature and particle
nature are liked by the de Broglie relation λ = h/p, where λ is the wavelength
of matter waves, also called de Broglie waves / Schrodinger waves, p is the
magnitude of the momentum of a particle or quantum of radiation and h is the
universal constant called Planck’s constant.
[Note : It is the smallness of h (= 6.63 × 10-34 J∙s)
that is very significant in wave-particle duality.]
Question 3.
Explain the inverse linear dependence of stopping potential on the incident
wavelength in a photoelectric effect experiment.
Answer:
Question 4.
It is observed in an experiment on photoelectric effect that an increase in the
intensity of the incident radiation does not change the maximum kinetic energy
of the electrons. Where does the extra energy of the incident radiation go? Is
it lost? State your answer with explanatory reasoning.
Answer:
When electromagnetic radiation with frequency greater than the threshold
frequency is incident on a metal surface, there is emission of electrons. It is
observed that not every incident photon is effective in liberating an electron.
In fact, the number of electrons emitted per second is far less than the number
of photons incident per second. The photons that are not effective in
liberation of electrons are reflected (or scattered) or absorbed resulting in
rise in the temperature of the metal surface. The maximum kinetic energy of a
photoelectron depends on the frequency of the incident radiation and the
threshold frequency for the metal. It has nothing to do with the intensity of
the incident radiation. The increase in intensity results in increase in the
number of electrons emitted per second.
Question 5.
Explain what do you understand by the de Broglie wavelength of an electron.
Will an electron at rest have an associated de Broglie wavelength? Justify your
answer.
Answer:
Under certain conditions an electron exhibits wave nature. Waves associated
with a moving electron are called matter waves or de Broglie waves or-
Schrodinger waves. The de Broglie wavelength of these matter waves is given by
X = h/p, where h is Planck’s constant and p is the magnitude of the momentum of
the electron.
If an electron is at rest, its momentum would be zero, and
hence the corresponding de Broglie wavelength would be infinite indicating
absence of a matter wave. However, according to quantum mechanics/wave
mechanics, this is not possible.
Question 6.
State the importance of Davisson and Germer experiment.
Answer:
The Davisson and Germer experiment directly indicated the wave nature of
material particles and quantitatively verified the de Broglie hypothesis for
the existence of matter waves.
[Note : The aim of the experiment was not to verify wave
like properties of electrons. The realisation came only later, an example of
serendipity.]
[Note : Like X-rays, electrons exhibit wave nature under
suitable conditions. When the wavelength of matter waves associated with moving
electrons is comparable to the inter-atomic spacing in a crystal, electrons
show diffraction effects. In 1927, Sir George Thomson (1892 – 1975), British
physicist, with his student Alex Reid, observed electron diffraction with a
metal foil. It is found that neutrons, atoms, molecules, Œ-particles, etc. show
wave nature under suitable conditions.]
Question 7.
What will be the energy of each photon in monochromatic light of frequency 5 ×
1014 Hz?
Answer:
Question 8.
Observations from an experiment on photoelectric effect for the stopping
potential by varying the incident frequency were plotted. The slope of the
linear curve was found to be approximately 4.1 × 10-15 V s.
Given that the charge of an electron is 1.6 × 10-19 C, find the
value of the Planck’s constant h.
Answer:
Question 9.
The threshold wavelength of tungsten is 2.76 × 10-5 cm. (a)
Explain why no photoelectrons are emitted when the wavelength is more than 2.76
× 10-5 cm.(b) What will be the maximum kinetic energy of
electrons ejected in each of the following cases
(i) if ultraviolet radiation of wavelength λ = 1.80 × 10-5 cm
and
(ii) radiation of frequency 4 × 1015 Hz is made incident on the
tungsten surface.
Answer:
Data: λ0 = 2.76 × 10-5 cm = 2.76 × 10-7 m,
λ =1.80 × 10-5 cm = 1.80 × 10-7 m,
v = 4 × 1015 Hz, h = 6.63 × 10-34 J∙s,c = 3 ×
108 m/s
(a) For λ > λ0, v < v0 (threshold frequency).
∴
hv < hv0. Hence, no photoelectrons are emitted.
Question 10.
Photocurrent recorded in the micro ammeter in an experimental set-up of
photoelectric effect vanishes when the retarding potential is more than 0.8 V
if the wavelength of incident radiation is 4950 Å. If the source of incident
radiation is changed, the stopping potential turns out to be 1.2 V. Find the
work function of the cathode material and the wavelength of the second source.
Answer:
∴
The work function of the cathode material,
Question 11.
Radiation of wavelength 4500 Å is incident on a metal having work function 2.0
eV. Due to the presence of a magnetic field B, the most energetic
photoelectrons emitted in a direction perpendicular to the field move along a
circular path of radius 20 cm. What is the value of the magnetic field B?
Answer:
Data: λ = 4500Å = 4.5 × 10-7 m,
Φ = 2.0eV = 2 × 1.6 × 10-19 J = 3.2 × 10-19 J,
h = 6.63 × 10-34 J∙s, c = 3 × 108 m/s,
r = 20 cm = 0.2 m, e= 1.6 × 10-19 C,
m = 9.1 × 10-31kg
This is the value of the magnetic field.
Question 12.
Given the following data for incident wavelength and the stopping potential
obtained from an experiment on photoelectric effect, estimate the value of
Planck’s constant and the work function of the cathode material. What is the
threshold frequency and corresponding wavelength? What is the most likely metal
used for emitter?
Answer:
Question 13.
Calculate the wavelength associated with an electron, its momentum and speed
(a) when it is accelerated through a potential of 54 V
Answer:
(b) when it is moving with kinetic energy of 150 eV.
Answer:
Question 14.
The de Broglie wavelengths associated with an electron and a proton are same.
What will be the ratio of
(i) their momenta
(ii) their kinetic energies?
Answer:
Question 15.
Two particles have the same de Broglie wavelength and one is moving four times
as fast as the other. If the slower particle
is an α-particle, what are the possibilities for the other particle?
Answer:
Question 16.
What is the speed of a proton having de Broglie wavelength of 0.08 Å?
Answer:
Question 17.
In nuclear reactors, neutrons travel with energies of 5 × 10-21 J.
Find their speed and wavelength.
Answer:
Question 18.
Find the ratio of the de Broglie wavelengths of an electron and a proton when
both are moving with the (a) same speed, (b) same energy and (c) same momentum?
State which of the two will have the longer wavelength in each case?
Answer:
Data: mp = 1836 me
Questions and Answers
Remember This (Textbook Page No. 316)
Question 1.
Is solar cell a photocell?
Answer:
Yes
Remember This (Textbook Page No. 317)
Question 1.
Can you estimate the de Broglie wavelength of the Earth?
Answer:
Taking the mass of the Earth as (about) 6 × 1024 kg, and the
linear speed of the earth around the Sun as (about) 3 × 104 m/s,
we have, the de Brogue wave length of the Earth as
Question 2.
The expression p = E/c defines the momentum of a photon. Can this expression be
used for momentum of an electron or proton?
Answer:
No
Remember This (Textbook Page No. 319)
Diffraction results described above can be produced in the
laboratory using an electron diffraction tube as shown in figure. It has a
filament which on heating produces electrons. This filament acts as a cathode.
Electrons are accelerated to quite high speeds by creating large potential
difference between the cathode and a positive electrode. On its way, the beam
of electrons comes across a thin sheet of
graphite. The electrons are diffracted by the atomic layers in the graphite and
form diffraction rings on the phosphor screen. By changing the voltage between
the cathode and anode, the energy, and therefore the speed, of the electrons
can be changed. This will change the wavelength of the electrons and a change
will be seen in the diffraction pattern. By increasing the voltage, the radius
of the diffraction rings will decrease. Try to explain why?
Answer:
When the accelerating voltage is increased, the kinetic energy and hence the
momentum of the electron increases. This decreases the de Brogue wavelength of
the electron. Hence, the radius of the diffraction ring decreases.
Remember This (Textbook Page No. 320)
Question 1.
On what scale or under which circumstances are the wave nature of matter
apparent?
Answer:
When the de Brogue wavelength of a particle such as an electron, atom, or
molecule is comparable to the interatomic spacing in a crystal, the wave nature
of matter is revealed in diffraction/interference.