CBSE Class 12 Physics Dual Nature And Radiation Boards Questions Worksheet

Question. Cathode ray consists of
a. Photons
b. Electrons
c. Protons
d. α-particles
Answer. B

Question. In which of the following, emission of electrons does not take place?
a. Thermionic emission
b. X-rays emission
c. Photoelectric emission
d. Secondary emission
Answer. B

Question. Which of the following when falls on a metal will emit photo electrons?
a. UV radiations
b. Infrared radiation
c. Radio waves
d. Microwaves
Answer. A

Question. The slope of stopping potential vs frequency of the incident light graph is
a. e/h
b. h/e
c. h/c
d. c/h
Answer. B

Question. Photoelectric effect shows
a. wave like behaviour of light
b. particle like behaviour of light
c. both wavelike and particle like behavior
d. neither wave like nor particle like behaviour of light.
Answer. B

Question. An electron and a proton have the same de Broglie wave length. Which of them have greater velocity.
a. Electron
b. proton.
c. both a and b
d. none of the above
Answer. A

1 Marks Questions

Question. If the wavelength of an electromagnetic radiation is doubled what will happen to the energy of photons?
Answer. Energy of photon reduces to one half.

Question. Two metals A and B have work functions 4 eV and 10 eV, respectively. Which metal has higher threshold wavelength?
Answer. Wavelength is inversely proportional to work function, so metal A with lower work function has higher threshold wavelength.

Question. What is the momentum of a photon of energy 1 MeV?
Answer. Energy E = 1 MeV = 1.6 x 10 ^-13J, p = E/c= 5.33x 10^-22Kg m/s

Question. Electrons are emitted from a photosensitive surface when it is illuminated by green light but electron emission does not take place by yellow light. Will the electrons be emitted when the surface is illuminated by (i) red light, (ii) blue light?
Answer. Since electron ejection is difficult from copper than sodium, so copper has greater work function than sodium. As threshold wavelength is inversely related with work function, so sodium has higher threshold wavelength than copper.

Question. A proton, a neutron, an electron and an α particle have same energy. Then their de- Broglie wavelengths compare as?
Answer. λ α 1/√m m_α > m_p = m_n > m_e, λ_e < λ_p = λ_n > λ_α

Question. Why do we not observe the phenomenon of photoelectric effect with non-metals?
Answer. Non-metals have high work function.

2 Marks Questions

Question. An electron is accelerated through a potential difference of 100 volt. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond?
Answer. 
λ = 1.227/√V nm = 1.227/√100 =1.227A⁰
X rays

Question. The graph shows variation of stopping potential Vo verses frequency of incident radiation ϑ for two photosensitive metals A and B
Answer. 
(i) From Einstein photoelectric equation,
eV₀ = h𝜈- ϕ0 or
V₀ =h𝜈/e − ϕ0/e
It is an equation of straight line as shown by line of A and B in figure
∴ slope of the line AB = ΔV₀/Δ𝜈 = h/e also threshold frequency is value from origin to point where line meets /cuts frequency axis.
Hence from the graph, the threshold frequency of Metal A is greater than the Metal B, therefore the work function of Metal A is more than Metal B
(ii) Intercept on potential axis = − ϕ₀/e from the equation Where, Work function = ϕ₀, e = charge of electron

Question. What is the effect of wavelength of incident photons on velocity of photoelectrons?
A beam of monochromatic radiation is incident on a photosensitive surface. Do the emitted photoelectrons have the same kinetic energy ? Explain
Answer. No, the different electrons belong to different energy level in conduction band. They need different energies to come out of the metal surface. For the same incident radiation, electrons knocked off from different energy levels come out with different energies.

Question. In an experiment on photoelectric emission, following observations were made 1) Wavelength of the incident light = 2 × 10^–7 m ²) Stopping potential = 3 V Find (i) kinetic energy of photoelectrons with maximum speed (ii) work function
Answer. 
Vs = 3 V and Kmax = eVo, so Kmax = 3 eV
(ii) λ = 2000 Å = 2 × 10^–7m.
Energy of incident photon = hc/ λ = 6.6 x 10^-34x 3 x 10⁸ / 2 × 10^–7 = 6.20 eV
W = E – Kmax = 3.2 eV

3 Marks Questions

Question. The work function of Caesium metal is 2.14eV. When light of frequency 6 x 10¹⁴Hz is incident on the metal surface photoemission of electrons occurs.
a. What is the maximum kinetic energy of the emitted photoelectrons
b. stopping potential
c. maximum speed of the emitted photoelectrons
Answer. Kmax = hv – ϕ₀
i) 6.63x10^-34x 6 x10¹⁴/1.6x10^-19 – 2.14eV = 0.314eV
ii) eV₀ = Kmax = 0.314eV V₀ = 0.314V
iii) 345.8 X 10³ m/s

Question. Define the terms (i) cut-off voltage and (ii) threshold frequency in relation to the Phenomenon of photoelectric effect. Using Einstein’s photoelectric equation show how the cut -off voltage and threshold frequency for a given photosensitive material can be determined with the help of a suitable plot.
Answer. Definitions.
From Einstein’s photoelectric equation, eV₀ = hν – φ₀ for ν > ν₀.
Cut off voltage V₀ = (h/e) ν – (φ0/e )
h/e is the slope of the graph.
ν₀ = φ₀/h

Question. The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?
Answer. E = hc/λ =6.6×10⁻³⁴×3×10⁸ / 330 x10^-9 = 3.767eV ϕ_o = 4.2eV since E < W₀ no photoelectric emission

Question. X-rays of wavelength fall on a photo sensitive surface emitting electrons. Assume that the work function of the metal can be neglected, prove that the de-Broglie wave length of the emitted electron will be √hλ/2mc.
Answer. As x ray photon of wavelength λ is incident on the metal surface, so KE of electrons KEmax= hc/λ (since, work function is negligible)
De Broglie wavelength of emitted electron, λ’= h / √ (2mKE_max) But, KE_max = hc/λ
So, λ’=h/ √(2m(hc/λ))=√(hλ/2mc)

Question. An electron and a photon each have a wavelength 10^-9 m. Find (i) Their momenta (ii) The energy of the photon and (iii) The kinetic energy of electron.
Answer. p= h/λ = 6.63x10^-25 m (ii) 𝐸= hc/λ= 1243 eV (iii) 𝐸= 𝑝2/2m= 1.52 eV.

Question. Light of wavelength 2000 A0 falls on an aluminum surface. In aluminum 4.2 eV are required to remove an electron. What is the kinetic energy of (a) fastest (b) the slowest photoelectron?
Answer. Given wavelength is λ = 2000A^o = 2×10⁻⁷ mϕ_o= 4.2eV.
(a) The kinetic energy is K.E_max = 1/2mv²max = hv−½ mV²max= hc/λ−ϕo = (6.6×10⁻³⁴×3×10⁸ /2×10⁻⁷)−4.2
½ mV²_max = 2eV This is the K.E of the fastest electron is 2eV
(b) The velocity of the slowest electron would be zero, hence the kinetic energy it possesses is also zero.

Question. A beam of monochromatic radiation is incident on a photosensitive Surface. Answer the following questions giving reasons.
a. Do the emitted photoelectrons have the same kinetic energy?
b. Does the kinetic energy of the emitted electrons depend on the intensity of incident radiation?
c. On what factors does the number of emitted photoelectrons depend?
Answer. 
a) No kinetic energy or photoelectrons depends on the energy level from which it comes out. Electrons from different energy levels beer different kinetic energies.
b) No kinetic energy depends on the energy of each photon only and not on the number of photons (i.e. intensity of light)
c) The number of photoelectrons depends on the intensity of incident light.

CASE BASED QUESTIONS:

1. According to wave theory of light, the light of any frequency can emit electrons from metallic surface provided the intensity of light be sufficient to provide necessary energy for emission of electrons, but according to experimental observations, the light of frequency less than threshold frequency cannot emit electrons; whatever be the intensity of incident light. Einstein also proposed that electromagnetic radiation is quantized.
If photoelectrons are ejected from a surface when light of wavelength λ1 = 550 nm is incident on it. The stopping potential for such electrons is Vs =0.19. If photoelectrons are ejected from a surface when light of wavelength λ1 = 550 nm is incident on it. The stopping potential for such electrons is Vs =0.19. Suppose the radiation of wavelength λ2 = 190 nm is incident on the surface.

Question. Photoelectric effect supports quantum nature of light because
a. there is a minimum frequency of light below which no photoelectrons are emitted.
b. the maximum K.E. of photoelectric depends only on the frequency of light and not on its intensity
c. even when the metal surface is faintly illuminated, the photo electrons leave the surface immediately.
d. electric charge of the photoelectrons is quantized.
Answer. A

Question. In photoelectric effect, electrons are ejected from metals, if the incident light has a certain minimum
a. Wavelength
b. Frequency
c. Amplitude
d. angle of incidence
Answer. B

Question. Calculate the stopping potential Vs2 of surface.
a. 4.47
b. 3.16
c. 2.76
d. 5.28
Answer. A

Question. Calculate the work function of the surface
a. 3.75
b. 2.07
c. 4.20
d. 3.60
Answer. B

Question. Calculate the threshold frequency for the surface
a. 500 x 10¹² Hz
b. 480 x 10¹³ Hz
c. 520 x 10¹¹ Hz
d. 460 x 10¹³ Hz
Answer. A

2. Lenard observed that when ultraviolet radiations were allowed to fall on the emitter plate of an evacuated glass tube, enclosing two electrodes (metal plates), current started flowing in the circuit connecting the plates. As soon as the ultraviolet radiations were stopped, the current flow also stopped. These observations proved that it was ultraviolet radiations, falling on the emitter plate, that ejected some charged particles from the emitter and the positive plate attracted them.

Question. Alkali metals like Li, Na, K and Cs show photo electric effect with visible light but metals like Zn, Cd and Mg respond to ultraviolet light. Why?
a. Frequency of visible light is more than that for ultraviolet light
b. Frequency of visible light is less than that for ultraviolet light
c. Frequency of visible light is same for ultraviolet light
d. Stopping potential for visible light is more than that for ultraviolet light
Answer. B

Question. Why do we not observe the phenomenon of photoelectric effect with non-metals?
a. For non-metals the work function is high
b. Work function is low
c. Work function can’t be calculated
d. For non-metals, threshold frequency is low
Answer. A

Question. What is the effect of increase in intensity on photoelectric current?
a. Photoelectric current increases
b. Decreases
c. No change
d. Varies with the square of intensity
Answer. A

Question. Name one factor on which the stopping potential depends
a. Work function
b. Frequency
c. Current
d. Energy of photon
Answer. B

Question. How does the maximum K.E of the electrons emitted vary with the work function of metal?
a. It doesn’t depend on work function
b. It decreases as the work function increases
c. It increases as the work function increases
d. It’s value is doubled with the work function
Answer. A

3. According to de-Broglie a moving material particle sometimes acts as a wave and sometimes as a particle or a wave is associated with moving material particle which controls the particle in every respect. The wave associated with moving material particle is called matter wave or de-Broglie wave whose wavelength called de-Broglie wavelength, is given by λ = h/mv

Question. The dual nature of light is exhibited by
a. diffraction and photo electric effect
b. photoelectric effect
c. refraction and interference
d. diffraction and reflection
Answer. A

Question. If the momentum of a particle is doubled, then its de-Broglie wavelength will
a. remain unchanged
b. become four times
c. become two times
d. become half
Answer. D

Question. If an electron and proton are propagating in the form of waves having the same λ , it implies that they have the same
a. Energy
b. Momentum
c. Velocity
d. angular momentum
Answer. B

Question. Velocity of a body of mass m, having de-Broglie wavelength λ , is given by relation
a. v = λ h/m
b. v = λm/h
c. v = λ/hm
d. v = h/ λm
Answer. D

Question. Moving with the same velocity, which of the following has the longest de Broglie wavelength?
a. ᵦ -particle
b. α -particle
c. proton
d. neutron
Answer. A