MHT-CET PYQs 2024 - Physics: Dual Nature of Radiation & Matter
Dual Nature of Radiation and Matter
1. A point source of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, then the stopping potential will
[MHT-CET 2024, May 16, Shift 2]
(1) increase
(2) decrease
(3) remain constant
(4) either increase or decrease
- If the frequency of incident radiation (v) is increased, keeping other factors constant, the stopping potential (v > \( v_0 \), threshold frequency)
(1) increases
(2) decreases
(3) remains constant
(4) suddenly becomes zero
- The number of photoelectrons emitted for light of frequency υ (higher than the threshold frequency ( \( v_0 \) ) is proportional to
(1) threshold frequency ( \( υ_0 \) )
(2) intensity of light (I)
(3) frequency of light (υ)
(4) work function ( \( ϕ_0 \) )
- In photoelectric effect, the photocurrent
(1) decreases with increase in frequency of incident photon
(2) increases with increase in frequency of incident photon
(3) does not depend on the frequency of photon but depends only on the intensity of incident light
(4) depends both on intensity and frequency of incident radiation
- Calculate wave length for emission of a photon having wave number 11516 \( cm^{-1} \).
(1) 216 nm
(2) 434 nm
(3) 868 nm
(4) 642 nm
- For a photosensitive material, work function is ‘\( W_0 \)’ and stopping potential is ‘V’. The wavelength of incident radiation is (h = Planck’s constant, c = velocity of light, e = electronic charge)
[MHT-CET 2024, May 4, Shift 1]
(1) \( \frac{h^2c^2}{W_o + eV} \)
(2) \( \frac{hc}{W_o} \)
(3) \( \frac{hcV}{W_o} \)
(4) \( \frac{hc}{W_o + eV} \)
- The frequency of incident light falling on a photosensitive material is doubled, the K.E. of the emitted photoelectrons will be
(1) unchanged
(2) two times its initial value
(3) more than two times its initial value
(4) less than two times its initial value
- When photons of energy hv fall on a photosensitive surface of work function \( E_0 \), photoelectrons of maximum energy k are emitted. If the frequency of radiation is doubled the maximum kinetic energy will be equal to (h = Planck’s constant)
(1) k
(2) 2k
(3) k + \( E_0 \)
(4) k + hv
- Using Einstein’s photoelectric equation, the graph between kinetic energy of emitted photoelectrons and the frequency of incident radiation is shown correctly by graph :
(1)
(2)
(3)
(4)
- The graph of stopping potential ‘\( V_s \)’ against frequency ‘v’ of incident radiation is plotted for two different metals ‘X’ and ‘Y’ as shown in graph. ‘\( ϕ_x \)’ and ‘\( ϕ_y \)’ are work functions of ‘X’ and ‘Y’ respectively then
(1) \( ϕ_x \) = \( ϕ_y \)
(2) \( ϕ_x \) < \( ϕ_y \)
(3) \( ϕ_x \) > \( ϕ_y \)
(4) \( ϕ_x \) = \( ϕ_y \) = 0
- In case of photoelectric effect, the graph of measured stopping potential (\( V_0 \)) against frequency ‘v’ of incident light is a straight line. The slope of this line multiplied by the charge of electron (e) gives
(1) the work function of the metal
(2) the Planck’s constant
(3) the maximum kinetic energy of the ejected electrons
(4) the threshold frequency for photoejection from the metal
- The stopping potential as a function of frequency of incident radiation is plotted for two different photoelectric surfaces A and B. The graph shows that the work function of A is
(1) greater than that of B
(2) smaller than that of B
(3) same as that of B
(4) that no comparison can be made from the graphs
- The figure shows the variation of photocurrent with anode potential for four different radiations. Let \( f_a \), \( f_b \), \( f_c \) and \( f_d \) be the frequencies for the curves a, b, c and d respectively
(1) \( f_a \) > \( f_b \) > \( f_c \) > \( f_d \)
(2) \( f_a \) < \( f_b \) < \( f_c \) < \( f_d \)
(3) \( f_a \) > \( f_b \) < \( f_c \) = \( f_d \)
(4) \( f_a \) = \( f_b \) > \( f_c \) > \( f_d \)
- The figure shows the variation of photocurrent with anode potential for four different radiations. Let \( I_a \), \( I_b \), \( I_c \) and \( I_d \) be the intensities for the curves a, b, c and d respectively. Then [\( f_a \), \( f_b \), \( f_c \) and \( f_d \) are frequencies respectively]
(1) \( f_a \) = \( f_b \) > \( f_c \) > \( f_d \) and \( I_a \)= \( I_b \) > \( I_c \) > \( I_d \)
(2) \( f_a \) < \( f_b \) > \( f_c \) = \( f_d \) and \( I_a \)= \( I_b \) > \( I_c \) > \( I_d \)
(3) \( f_a \) = \( f_b \) = \( f_c \) = \( f_d \) and \( I_a \)< \( I_b \) < \( I_c \) < \( I_d \)
(4) \( f_a \) > \( f_b \) > \( f_c \) > \( f_d \) and \( I_a \)= \( I_b \) = \( I_c \) = \( I_d \)
- When a photosensitive surface is irradiated by lights of wavelengths '\( λ_1 \)' and ‘\( λ_2 \)’, kinetic energies of the emitted photoelectrons is ‘\( E_1 \)’ and ‘\( E_2 \)’ respectively. The work function of the photosensitive surface is
(1) \( \frac{ ( E_2λ_2 - E_1λ_1 ) }{ ( λ_2 - λ_1 ) } \)
(2) \( \frac{ ( E_1λ_1 + E_2λ_2 ) }{ ( λ_2 - λ_1 ) } \)
(3) \( \frac{ ( E_1λ_1 - E_2λ_2 ) }{ ( λ_2 - λ_1 ) } \)
(4) \( \frac{ ( E_2λ_2 + E_1λ_1 ) }{ ( λ_1 - λ_2 ) } \)
- Two identical photocathodes receive light of frequencies ‘\( n_1 \)’ and ‘\( n_2 \)’. If the velocities of the emitted photoelectrons of mass ‘m’ are ‘\( V_1 \)’ and ‘\( V_2 \)’ respectively, then (h = Planck’s constant)
(1) \( V_1 + V_2 = [ \frac{2h}{m} ( n_1 + n_2 ) ]^{1/2} \)
(2) \( V_1 - V_2 = [ \frac{2h}{m} ( n_1 - n_2 ) ]^{1/2} \)
(3) \( V_1^2 + V_2^2 = \frac{2h}{m} ( n_1 + n_2 ) \)
(4) \( V_1^2 - V_2^2 = \frac{2h}{m} ( n_1 - n_2 ) \)
- The work function of metal ‘A’ and ‘B’ are in the ratio 1 : 2. If light of frequency ‘f ’ and ‘2f ’ is incident on surface ‘A’ and ‘B’ respectively, then the ratio of kinetic energies of emitted photo electrons is
(1) 1 : 1
(2) 1 : 2
(3) 1 : 3
(4) 1 : 4
- A photoelectric surface is illuminated successively by monochromatic light of wavelength λ and (λ/3). If the maximum kinetic energy of the emitted photoelectrons in the second case is 4 times that in the first case, the work function of the surface of the material is (h = Planck’s constant, c = speed of light)
(1) \( \frac{hc}{λ} \)
(2) \( \frac{hc}{2λ} \)
(3) \( \frac{hc}{3λ} \)
(4) \( \frac{3hc}{λ} \)
- A photoelectric surface is illuminated successively by monochromatic light of wavelength ‘λ’ and (\( \frac{λ}{2} \) ) . If the maximum kinetic energy of the emitted photoelectrons in the first case is one-fourth that in the second case, the work function of the surface of the material is (c = speed of light, h = Planck’s constant)
(1) \( \frac{2hc}{λ} \)
(2) \( \frac{hc}{λ} \)
(3) \( \frac{2hc}{3λ} \)
(4) \( \frac{hc}{3λ} \)
- When a metallic surface is illuminated with a radiation of wavelength ‘λ’, the stopping potential is ‘V’. If the same surface is illuminated with radiation of wavelength ‘3λ’, the stopping potential is (\( \frac{V}{6} \) ). The threshold wavelength for the surface is
[MHT-CET 2024, May 2, Shift 1]
(1) 3λ
(2) 4λ
(3) 5λ
(4) 6λ
- When a certain metallic surface is illuminated with monochromatic light wavelength λ, the stopping potential for photoelectric current is 4\( V_0 \). When the same surface is illuminated with light of wavelength 3λ, the stopping potential is \( V_0 \). The threshold wavelength for this surface for photoelectric effect is
[MHT-CET 2024, May 15, Shift 2]
(1) 9λ
(2) \( \frac{λ}{9} \)
(3) 3λ
(4) \( \frac{λ}{3} \)
- The threshold frequency of a metal is ‘\( F_0 \)’. When light of frequency 2\( F_0 \) is incident on the metal plate, the maximum velocity of photoelectron is ‘\( V_1 \)’. When the frequency of incident radiation is increased to ‘5\( F_0 \)’, the maximum velocity of photoelectrons emitted is ‘\( V_2 \)’. The ratio of \( V_1 \) and \( V_2 \) is
[MHT-CET 2024, May 4, Shift 1]
(1) \( \frac{1}{8} \)
(2) \( \frac{1}{16} \)
(3) \( \frac{1}{4} \)
(4) \( \frac{1}{2} \)
- A photosensitive metallic surface has work function ϕ. If photon of energy 3ϕ falls on the surface, the electron comes out with a maximum velocity of 6 × \( 10^6 \) m/s. When the photon energy is increased to 9ϕ, then maximum velocity of photoelectrons will be
(1) 12 × \( 10^6 \) m/s
(2) 6 × \( 10^6 \) m/s
(3) 3 × \( 10^6 \) m/s
(4) 24 × \( 10^6 \) m/s
- The kinetic energy of an electron is increased by 2 times, then the de-Broglie wavelength associated with it changes by a factor
(1) \( \frac{1}{3} \)
(2) \( \frac{1}{\sqrt3} \)
(3) 3
(4) \( \sqrt{3} \)
- If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength (λ) associated with the electrons change?
(1) λ is increased to \( \sqrt2 \) times
(2) λ is increased to \( \frac{1}{\sqrt2} \) times
(3) λ is decreased to \( \frac{1}{\sqrt2} \) times
(4) λ is decreased to \( \sqrt2 \) times
- If the potential difference used to accelerate electrons is increased four times, by what factor does the de-Broglie wavelength associated with the electrons change?
(1) Wavelength increased two times
(2) Wavelength decreased to half
(3) Wavelength increased four times
(4) Wavelength remains the same
- The ratio of the wavelength of a photon of energy E to that of the electron of same energy is (m = mass of an electron, c = speed of light, h = Planck’s constant)
(1) \( \sqrt{\frac{m}{CE}} \)
(2) \( \sqrt{\frac{2m}{CE}} \)
(3) \( C \sqrt{\frac{m}{E}} \)
(4) \( C \sqrt{\frac{2m}{E}} \)
- Kinetic energy of a proton is equal to energy E of a photon. Let ' \( λ_1 \) ' be the de-Broglie wavelength of proton and ' \( λ_2 \) ' be the wavelength of photon. If \( ( \frac{λ_1}{λ_2} )αE^n \) , then the value of n is
(1) 1
(2) 2
(3) 5
(4) 0.5
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