Multiple Choice & Assertion-Reason

PHYExam Practice

This is a chapter-wide revision article for the objective and assertion-reason questions on dual nature. The MCQs cross-link three ideas: the photon picture of light ( $E=hf=hc/\lambda$ , $p=h/\lambda$ ), Einstein's photoelectric equation ( $K_{max}=hf-\phi_0$ ), and the de Broglie hypothesis ( $\lambda=h/p$ ).

Examiners test whether you can tell which quantity depends on frequency versus intensity, recall landmark experiments (Davisson-Germer for electron waves), and reason carefully in assertion-reason format where both statements can be true yet unrelated.

Photon energy

E = h f = \dfrac{h c}{\lambda}

E

= photon energy (J),

h=6.63\times10^{-34}

J s,

f

= frequency (Hz),

c=3\times10^{8}

m/s,

\lambda

= wavelength (m). Divide by

1.6\times10^{-19}

to get eV.

Photon momentum

p = \dfrac{E}{c} = \dfrac{h}{\lambda}

p

= photon momentum (kg m/s). A photon has zero rest mass but carries momentum

h/\lambda

Einstein photoelectric equation

K_{max} = h f - \phi_0 = e V_0

K_{max}

= maximum KE of photoelectrons,

\phi_0

= work function,

V_0

= stopping potential,

e=1.6\times10^{-19}

C. Only frequency (not intensity) sets

K_{max}

de Broglie wavelength

\lambda = \dfrac{h}{p} = \dfrac{h}{\sqrt{2 m K}}

\lambda

= matter wavelength,

p

= momentum,

m

= mass,

K

= kinetic energy. For equal

K

\lambda \propto 1/\sqrt{m}

Threshold relations

\phi_0 = h f_0 = \dfrac{h c}{\lambda_0}

f_0

= threshold frequency,

\lambda_0

= threshold wavelength. Useful shortcut:

\lambda_0(\text{nm}) \approx 1240 / \phi_0(\text{eV})

Photon energy is directly proportional to frequency and inversely proportional to wavelength: $E=hc/\lambda$ . A common option trap is $hc\lambda$ or $h\lambda/c$ , both dimensionally wrong.
Photoelectric $K_{max}$ depends only on frequency (and the metal's $\phi_0$ ); intensity controls the number of photoelectrons, hence the photocurrent, not their energy.
Stopping potential $V_0$ satisfies $eV_0=hf-\phi_0$ , so $V_0$ rises linearly with $f$ but is NOT proportional to $f$ (the intercept $-\phi_0/e$ means doubling $f$ more-than-doubles $V_0$ ).
Useful constants: $hc \approx 1240$ eV nm, so a 2.0 eV work function gives $\lambda_0 \approx 620$ nm. Memorise this to answer threshold MCQs instantly.
For an electron accelerated through $V$ volts, $\lambda(\text{\AA}) \approx 12.27/\sqrt{V}$ , so 100 V gives about 1.23 \AA — a standard recall result.
For particles of the same kinetic energy $\lambda \propto 1/\sqrt{m}$ ; for the same speed $\lambda \propto 1/m$ ; for the same momentum $\lambda$ is identical.
The Davisson-Germer experiment (electron diffraction by a nickel crystal) confirmed the wave nature of electrons; it does not demonstrate the photoelectric effect or the neutron.
In assertion-reason questions, both A and R may be individually true while R is NOT the correct explanation — read each statement as a standalone fact before judging the causal link.

Where the marks go

Confusing what intensity changes (number of electrons / photocurrent) with what frequency changes ( $K_{max}$ and $V_0$ ) — the single most tested distinction.
Assuming stopping potential doubles when frequency doubles; because of the $-\phi_0$ intercept, $V_0$ increases by more than double above threshold.
Mixing eV and joule: forgetting to multiply or divide by $e=1.6\times10^{-19}$ when converting photon energies for MCQ numerics.
Using $\lambda \propto 1/\sqrt{m}$ for the wrong condition — it holds only at equal kinetic energy, not equal speed or equal momentum.

How the board asks it

Assertion–Reason $eV_0=hf-\phi_0$ intercept; $V_0$ linear in $f$ but not proportional
Assertion (A): When the frequency of incident radiation is doubled, the stopping potential of a photocell becomes more than double. Reason (R): The stopping potential is directly proportional to the frequency of the incident radiation. Choose the correct option among (a) both A and R are true and R is the correct explanation of A, (b) both are true but R is not the correct explanation, (c) A is true but R is false, (d) A is false but R is true.
Assertion–Reasonintensity sets photocurrent; frequency sets $K_{max}$
Assertion (A): On increasing the intensity of incident light while keeping its frequency fixed, the maximum kinetic energy of the emitted photoelectrons remains unchanged. Reason (R): The intensity of light fixes the number of photons incident per second, not the energy $hf$ carried by each photon. Choose the correct option among (a) both A and R are true and R is the correct explanation of A, (b) both are true but R is not the correct explanation, (c) A is true but R is false, (d) A is false but R is true.
Assertion–Reasondavisson-germer electron diffraction confirms wave nature
Assertion (A): The Davisson-Germer experiment established the wave nature of electrons. Reason (R): In the experiment a beam of electrons was diffracted by a nickel crystal, producing intensity maxima at definite angles. Choose the correct option among (a) both A and R are true and R is the correct explanation of A, (b) both are true but R is not the correct explanation, (c) A is true but R is false, (d) A is false but R is true.
Multiple choice $\lambda=h/p$ , $\lambda\propto 1/\sqrt{m}$ at equal $K$ ; $\lambda\approx 12.27/\sqrt{V}$ Å
A proton and an electron are accelerated from rest through the same potential difference. The de Broglie wavelength of the electron compared with that of the proton is (a) larger, because $\lambda\propto 1/\sqrt{m}$ for equal kinetic energy, (b) smaller, because the electron moves faster, (c) equal, because both carry the same charge magnitude, (d) zero. Select the correct option and justify the choice.
Give reasonsthreshold frequency; $K_{max}=hf-\phi_0$ depends on frequency only
A photocell shows no current however intense the incident red light, yet a feeble violet beam produces a current. Explain this observation using the photon picture, and state on what factor the maximum kinetic energy of the emitted photoelectrons depends.

Previousde Broglie Wavelength

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.