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Dual Nature of Radiation and Matter Set-3 MCQ Online Practice Test | Class 12 | Quiz Tweek

Dual Nature of Radiation and Matter Set-3

Practice Important MCQs for Dual Nature of Radiation and Matter — Physics, Class 12.

Mastery of the dual nature of radiation and matter is essential for the CBSE Board and competitive exams (JEE/NEET) because it links wave and particle descriptions through quantitative relations such as $E=hf$ , $p=h/\lambda$ and the Compton shift. Problems in this chapter test both conceptual understanding (how/when wave or particle pictures apply) and facility with numerical manipulations that appear frequently in competitive papers.

The questions that follow are designed to build skills in multi-step reasoning, graph/data interpretation and assertion–reason analysis. You will apply relations like $\Delta\lambda=\lambda_C(1-\cos\theta)$ and Bragg’s condition $2d\sin\theta=n\lambda$ , interpret I–V plots for photoelectric effect and connect diffraction limits with uncertainty — the mix mirrors Board and JEE/NEET style demands.

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Q1. An electron is accelerated from rest through a potential difference of $150\ \text{V}$ . Using $h=6.63\times10^{-34}\ \text{J\,s}$ and $m_e=9.11\times10^{-31}\ \text{kg}$ , its de Broglie wavelength is most nearly:

(A)

$1.00\times10^{-11}\ \text{m}$

(B)

$3.00\times10^{-10}\ \text{m}$

(C)

$1.00\times10^{-10}\ \text{m}$

(D)

$1.00\times10^{-9}\ \text{m}$

Q2. In a photoelectric experiment two I–V curves are recorded for the same metal using monochromatic light of the same frequency (above threshold). Curve (ii) corresponds to a higher light intensity than (i). The measured graphs show that both curves have the same stopping potential $V_0$ , while the saturation current for (ii) is larger than for (i). Which statement best explains these observations?

(A)

The stopping potential depends only on frequency; the larger saturation current for (ii) indicates higher photon flux (more electrons emitted per second).

(B)

The stopping potential is independent of intensity because photons in (ii) lose momentum upon emission; the saturation current is independent of photon flux.

(C)

Larger intensity in (ii) increases energy per photon causing higher kinetic energy of ejected electrons, so stopping potential should increase.

(D)

Higher intensity reduces the work function due to surface heating; hence saturation current increases but stopping potential decreases.

Q3. An X‑ray photon of wavelength $\lambda=0.050\ \text{nm}$ is Compton‑scattered by a free electron. If the scattering angle is $90^\circ$ , the wavelength of the scattered photon is most nearly (take $\lambda_C=\dfrac{h}{mc}=2.426\times10^{-12}\ \text{m}$ ):

(A)

$0.0476\ \text{nm}$

(B)

$0.0500\ \text{nm}$

(C)

$0.0548\ \text{nm}$

(D)

$0.0524\ \text{nm}$

Q4. Assertion (A): Using the non‑relativistic de Broglie relation $\lambda_e=\dfrac{h}{\sqrt{2mE}}$ for an electron and the photon wavelength $\lambda_\gamma=\dfrac{hc}{E}$ for a photon, equating $\lambda_e=\lambda_\gamma$ (electron and photon having the same energy $E$ ) yields $E=2mc^2$ .
Reason (R): The result $E=2mc^2$ is physically unacceptable because at energies comparable to $mc^2$ the electron is relativistic, so the non‑relativistic expression for $\lambda_e$ used in the derivation is invalid.

(A)

Both A and R are true and R is the correct explanation of A.

(B)

Both A and R are true but R is not the correct explanation of A.

(C)

A is true but R is false.

(D)

A is false but R is true.

Q5. In an electron diffraction experiment electrons are accelerated from rest through a potential $V$ and scattered by crystal planes with interplanar spacing $d=0.21\ \text{nm}$ . A first‑order ( $n=1$ ) Bragg peak is observed at angle $\theta=30^\circ$ satisfying $2d\sin\theta=n\lambda$ . Using $\lambda=\dfrac{h}{\sqrt{2meV}}$ , the accelerating potential $V$ (in volts) required is most nearly:

(A)

$10\ \text{V}$

(B)

$100\ \text{V}$

(C)

$34\ \text{V}$

(D)

$240\ \text{V}$

Q6. Assertion (A): For monochromatic light of frequency above threshold incident on a metal, increasing the intensity increases the saturation photocurrent but does not change the stopping potential.
Reason (R): The stopping potential depends only on photon frequency because the maximum kinetic energy of emitted electrons is $K_{\max}=h\nu-\phi$ , independent of the number of incident photons.

(A)

Both A and R are true and R is the correct explanation of A.

(B)

Both A and R are true but R is not the correct explanation of A.

(C)

A is true but R is false.

(D)

A is false but R is true.

Q7. A photon of wavelength $500\ \text{nm}$ and an electron accelerated through $100\ \text{V}$ are compared. Using $p_\gamma=\dfrac{h}{\lambda}$ for the photon and $p_e=\sqrt{2meV}$ for the electron, which statement is closest to the correct comparison of magnitudes?

(A)

$p_\gamma$ is larger than $p_e$ by about $4\times10^{3}$ .

(B)

$p_e$ and $p_\gamma$ are of the same order of magnitude.

(C)

$p_e$ is larger than $p_\gamma$ by about $4\times10^{6}$ .

(D)

$p_e$ is larger than $p_\gamma$ by about $4.1\times10^{3}$ .

Q8. A monochromatic X‑ray beam of wavelength $\lambda=0.050\ \text{nm}$ is Compton‑scattered by free electrons. The measured scattered wavelengths $\lambda'$ at scattering angles $\theta$ are:

\begin{array}{c|cccc} \theta(^{\circ}) & 0 & 60 & 120 & 180\\\hline \lambda'(\text{nm}) & 0.050000 & 0.051213 & 0.053639 & 0.0548526 \end{array}

Plotting $\Delta\lambda=\lambda'-\lambda$ vs $(1-\cos\theta)$ gives a straight line whose slope is the Compton wavelength $\lambda_C$ . From the table the experimental value of $\lambda_C$ (in metres) is most nearly:

(A)

$2.426\times10^{-12}\ \text{m}$

(B)

$2.426\times10^{-10}\ \text{m}$

(C)

$2.426\times10^{-9}\ \text{m}$

(D)

$2.426\times10^{-11}\ \text{m}$

Q9. A monoenergetic electron beam (fixed kinetic energy) passes through a single slit of width $a$ and produces a diffraction pattern on a distant screen; the width of the central maximum is $W$ . If the slit width is reduced to $a/2$ (all other parameters unchanged), which statement correctly describes the change on the screen and the electron's kinetic energy?

(A)

Central maximum becomes $W/2$ ; electron kinetic energy increases.

(B)

Central maximum becomes $W/2$ ; electron kinetic energy unchanged.

(C)

Central maximum becomes $2W$ ; electron kinetic energy unchanged.

(D)

Central maximum unchanged; electron kinetic energy decreases.

Q10. The stopping potential $V_s$ for photoelectrons emitted from a metal is measured for two incident light frequencies:

Frequency $f$ (× $10^{14}\ \text{Hz}$ ): $5.00,\ 7.00$
Stopping potential $V_s$ (V): $0.10,\ 0.927$

Using the photoelectric relation $eV_s=hf-\phi$ , an estimate of Planck's constant $h$ (in J·s) from the slope is most nearly:

(A)

$4.14\times10^{-34}\ \text{J\,s}$

(B)

$6.63\times10^{-34}\ \text{J\,s}$

(C)

$1.05\times10^{-33}\ \text{J\,s}$

(D)

$3.31\times10^{-34}\ \text{J\,s}$

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