# Unit-7, DUAL NATURE OF MATTER AND RADIATION Concepts and formula

```Unit-7, DUAL NATURE OF MATTER AND RADIATION
Concepts and formula
1. PHOTO ELECTRIC EFFECT
“The phenomenon of emission of electrons from mainly metal surfaces exposed to light energy of suitable
frequency is known as photoelectric effect.”
The electrons emitted by this effect are called photoelectrons. The current constituted by
photoelectrons is known as photoelectric current.
2. HERTZ AND LENARD’S OBSERVATIONS: All the graphs given in NCERT book are important.
3. Laws of Photoelectric Emission:
i)
For a given substance, there is a minimum value of frequency of incident light called threshold frequency below
which no photoelectric emission is possible, howsoever, the intensity of incident light may be.
ii)
The number of photoelectrons emitted per second (i.e. photoelectric current) is directly proportional to the
intensity of incident light provided the frequency is above the threshold frequency.
iii)
The maximum kinetic energy of the photoelectrons is directly proportional to the frequency, provided the
frequency is above the threshold frequency.
iv)
The maximum kinetic energy of the photoelectrons is independent of the intensity of the incident light.
v)
The process of photoelectric emission is instantaneous. i.e. as soon as the photon of suitable frequency falls on
the substance, it emits photoelectrons.
vi)
The photoelectric emission is one-to-one interaction between a photon of suitable frequency and an electron
of the metal.
4. Einsteins Photo electric relation
KEmax  h    h  h 0
h
5. Debroglie wave length:

c

h
c
0
h
h

p mv
6. DAVISSON –GERMER EXPERIMENT
OBSERVATIONS:
Intensity of scattered beam of electrons is found to be maximum when angle of scattering is 50° for all values of
gun potentials and this maximum is heighest for the gun potential 54 V.
CALCULATIONS
Wavelength of electron { for the first principal maximum (n=1)}as calculated from λ= 2d SinΘ(Bragg’s equation
valid for waves) is 1.65Å
Wavelength calculated by de Broglie’s formula for electron scattered with maximum intensity at gun potential
54V is
λ =h/mv =(12.27Å /√54)= 1.61Å( equation valid for material particles
CONCLUSION:
The values are in good agreement with each other.Hence wave nature of electrons is verified
VSA 1 mark questions
1.
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4.
5.
6.
7.
8.
What is photoelectric effect?
How does the photoelectric current vary with Intensity of incident light radiation?
What is the effect on kinetic energy of photoelectron with intensity of incident radiation of light?
What do you mean by stopping potential in reference to photoelectric emission?
Define threshold frequency for a photo sensitive surface
How does the kinetic energy of photoelectron get effected with frequency (i)if it is above threshold value ?
Can Maxwell’s electromagnetic theory of light explain photo electric emission?
Name the theory that could explain Photo electric effect and the scientist who proposed it
9. What is a photon?
10. The maximum kinetic energy of photoelectron is 2.8 eV. What is the value of
Stopping potential?
11. Stopping potential for a photosensitive surface is -2.5V. What is the maximum kinetic energy of photoelectron in
the photo electric emission from that surface
12. Name the scientist who proposed wave nature of matter
( 2 marks and 3 marks questions including numerical)
1. Calculate the energy in eV associated with a photon of wavelength 4000Ao?
2. Light of wavelength 2000Å falls on an aluminium surface. In aluminium 4.2 eV are required to remove an
electron. What is the kinetic energy of (a) fastest
(b) the slowest photoelectron?
3. The following table gives the values of work functions for a few sensitive metals.
If each of these metals is exposed to radiations of wavelength 3300nm, which of
these will not exit photoelectrons and why?
S. No.
1
2
3
Metal
Na
K
Mo
Work function(eV)
1.92
2.15
4.17
4. An electron has kinetic energy equal to 100eV. Calculate (1) momentum (2) speed (3) Debroglie wavelength of
the electron.
5. Calculate the threshold frequency of photon for photoelectric emission from a Metal of work function 0.1eV?
6. Photoelectrons are emitted with a maximum speed of 7x105m/s from a surface when light of frequency
8x1014Hz is incident on it. Find the threshold frequency for this surface?
7. A proton and an electron have energy 200eV each. Which one of these has greater de-Broglie wavelength
8. Find the ratio of de-Broglie wavelengths associated with two electrons A and B which are accelerated through
8V and 64V respectively.
9. Determine the velocity and kinetic energy of a neutron having de -Broglie wavelength 1Å. Given that mass of
neutron 1.67 X 10-27kg and h = 6.63 X 10-34J-s
10. Show that wavelength associated with a particle of mass m and kinetic energy E is given by
λ =
√
11. Plot the graph for variation of Photo electric current with
(a) Intensity of Incident radiation of light
(b) Potential of collector plate for the same intensity of light but different frequencies higher than the
threshold
(c) Potential of collector plate for the same frequency of light higher than the threshold but different
intensities
12. Plot the graph for variation of magnitude of stopping potential with the frequency of Incident radiation of light
VALUE BASED QUESTIONS
1. In a multistoried building, once a fire broke out at midnight due to electrical short
circuit.Ravi along with
others rushed to the spot, informed the fire servive and put off the fire. But by that time a huge amount of
damage had already been done. Ravi being Secretary of the building decided to fix fire alarms (using photo cell)
in all the floors
(i)What values were shown by Ravi in this situation?
(ii) A human eye can perceive a minimum light intensity is about 10-10 Wm-2 Calculate the number of photons
of wavelength 5.6 x 10-7 m/s that must enter the pupil of area 10-4m2
2. Ravi, while returning home from office late night, saw a person jumping into a house .Suspecting him to be a thief,
he slowly followed him. He saw an alarm fixed at the entry of the house. Immediately to alarm the people at the
house, he used his laser torch to activate the alarm, as it works with the visible light. The circuit became complete
and siren tarted working and people at the house got up and caught the thief. They thanked Ravi for his action.
a) What moral value can you see in Ravi?
b) The photoelectric cut off voltage in a certain experiment is 1.5V. What is the maximum kinetic energy of the
photoelectrons emitted?
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