Modern Physics flash cards

1. 1.What is the photoelectric effect?

   The emission of electrons from a metal surface when light of suitable frequency falls on it. The ejected electrons are called photoelectrons.

   Hint: Light in, electrons out.

2. 2.What is the work function $\phi_0$ of a metal?

   The minimum energy required to remove an electron from the metal surface. It equals $h\nu_0$, where $\nu_0$ is the threshold frequency.

   Hint: Minimum energy to free an electron.

3. 3.What is threshold frequency $\nu_0$?

   The minimum frequency of incident light below which no photoelectric emission occurs, no matter how intense the light. Related as $\phi_0 = h\nu_0$.

   Hint: Below it, no emission at all.

4. 4.Write Einstein's photoelectric equation.

   $K_{max} = h\nu - \phi_0$, where $K_{max}$ is the maximum kinetic energy of the emitted photoelectron and $\phi_0$ is the work function.

   Hint: KE = photon energy − work function.

5. 5.What is a photon?

   A quantum (packet) of light energy of magnitude $E = h\nu$. It has zero rest mass, travels at speed $c$, and carries momentum $p = h/\lambda$.

   Hint: Particle of light, $E=h\nu$.

6. 6.What is threshold wavelength $\lambda_0$?

   The maximum wavelength of incident light that can cause photoemission: $\lambda_0 = \dfrac{hc}{\phi_0}$. Longer wavelengths cannot eject electrons.

   Hint: Longest wavelength that still works.

7. 7.How does maximum KE of photoelectrons depend on frequency of light?

   $K_{max} = h\nu - \phi_0$, so $K_{max}$ increases linearly with frequency $\nu$ (for $\nu > \nu_0$) and is independent of light intensity.

   Hint: Linear in $\nu$, not intensity.

8. 8.How does photoelectric current depend on intensity of light?

   At a fixed frequency above threshold, the number of photoelectrons per second (and hence the current) is directly proportional to the intensity.

   Hint: More light → more electrons, same KE.

9. 9.What is stopping potential $V_0$?

   The minimum negative (retarding) potential applied to the collector at which the photoelectric current becomes zero. It satisfies $eV_0 = K_{max}$.

   Hint: Voltage that just stops the fastest electron.

10. 10.Relation between stopping potential and frequency?

    $eV_0 = h\nu - \phi_0$, so $V_0 = \dfrac{h}{e}\nu - \dfrac{\phi_0}{e}$. A graph of $V_0$ vs $\nu$ is a straight line of slope $h/e$.

    Hint: Slope of $V_0$–$\nu$ line is $h/e$.

11. 11.Does stopping potential depend on intensity of light?

    No. Stopping potential depends only on the frequency of light and the metal's work function, not on intensity.

    Hint: Frequency decides it, not brightness.

12. 12.Why does the photoelectric effect support the particle nature of light?

    Emission is instantaneous, depends on frequency (not intensity) with a threshold, and $K_{max}$ rises with $\nu$ — all explained by photons of energy $h\nu$, not by classical waves.

    Hint: Threshold + instant emission = photons.

13. 13.Why is there no time lag in the photoelectric effect?

    A single photon delivers its whole energy $h\nu$ to one electron in a single collision, so emission is essentially instantaneous ($<10^{-9}$ s).

    Hint: One photon, one electron, at once.

14. 14.What did classical wave theory fail to explain about the photoelectric effect?

    The existence of a threshold frequency, the independence of $K_{max}$ from intensity, and the instantaneous emission. Wave theory predicted energy build-up over time.

    Hint: Wave theory got threshold and timing wrong.

15. 15.What is the value of Planck's constant $h$?

    $h \approx 6.63 \times 10^{-34}$ J s. It relates a photon's energy to its frequency: $E = h\nu$.

    Hint: $6.63\times10^{-34}$ J s.

16. 16.What is 1 electron volt (eV) in joules?

    $1\ \text{eV} = 1.6 \times 10^{-19}$ J — the energy gained by an electron accelerated through a potential difference of 1 volt.

    Hint: $1.6\times10^{-19}$ J.

17. 17.State the dual nature of radiation.

    Light behaves as a wave (interference, diffraction, polarization) and as a stream of particles/photons (photoelectric effect, Compton effect). It exhibits wave–particle duality.

    Hint: Wave AND particle.

18. 18.What is de Broglie's hypothesis?

    Every moving particle of momentum $p$ has an associated matter wave of wavelength $\lambda = \dfrac{h}{p} = \dfrac{h}{mv}$.

    Hint: Matter has waves too.

19. 19.Write the de Broglie wavelength in terms of kinetic energy.

    For a particle of mass $m$ and kinetic energy $K$: $\lambda = \dfrac{h}{\sqrt{2mK}}$.

    Hint: $\lambda = h/\sqrt{2mK}$.

20. 20.de Broglie wavelength of an electron accelerated through potential $V$?

    $\lambda = \dfrac{h}{\sqrt{2meV}} \approx \dfrac{1.227}{\sqrt{V}}$ nm (with $V$ in volts).

    Hint: $\lambda \approx 1.227/\sqrt{V}$ nm.

21. 21.Why don't we observe the wave nature of a moving cricket ball?

    Its momentum is very large, so $\lambda = h/p$ is extremely small (much smaller than any aperture), making diffraction/interference unobservable.

    Hint: Huge $p$ → tiny $\lambda$.

22. 22.Which experiment confirmed the wave nature of electrons?

    The Davisson–Germer experiment, which showed electron diffraction from a nickel crystal, matching de Broglie's predicted wavelength.

    Hint: Davisson–Germer, electron diffraction.

23. 23.How does de Broglie wavelength change if a particle's speed increases?

    Since $\lambda = h/mv$, wavelength decreases as speed (momentum) increases; they are inversely related.

    Hint: Faster → shorter wave.

24. 24.For the same KE, which has a longer de Broglie wavelength: an electron or a proton?

    The electron. Since $\lambda = h/\sqrt{2mK}$, the smaller mass gives the longer wavelength for equal kinetic energy.

    Hint: Lighter particle, longer wave.

25. 25.What are the postulates of Bohr's model of hydrogen (in brief)?

    (1) Electrons orbit in stable stationary states without radiating. (2) Angular momentum is quantized: $L = mvr = \dfrac{nh}{2\pi}$. (3) Radiation is emitted/absorbed only when an electron jumps between orbits: $h\nu = E_i - E_f$.

    Hint: Stationary orbits, quantized $L$, jump = photon.

26. 26.State Bohr's quantization of angular momentum.

    The angular momentum of the electron is an integral multiple of $\dfrac{h}{2\pi}$: $mvr = \dfrac{nh}{2\pi}$, where $n = 1,2,3,\dots$

    Hint: $L = nh/2\pi$.

27. 27.What is the radius of the $n$th Bohr orbit of hydrogen?

    $r_n = \dfrac{n^2 h^2 \varepsilon_0}{\pi m e^2} = 0.529\, n^2$ Å. It increases as $n^2$.

    Hint: $r_n \propto n^2$; $r_1 = 0.53$ Å.

28. 28.What is the Bohr radius?

    The radius of the smallest ($n=1$) orbit of hydrogen: $a_0 = 0.529\ \text{Å} = 0.529 \times 10^{-10}$ m.

    Hint: Ground-state radius, $0.53$ Å.

29. 29.What is the energy of the $n$th level of hydrogen?

    $E_n = -\dfrac{13.6}{n^2}$ eV. The energy is negative (bound) and increases (toward 0) as $n$ increases.

    Hint: $E_n = -13.6/n^2$ eV.

30. 30.What is the ground-state energy of the hydrogen atom?

    $E_1 = -13.6$ eV. This is the most tightly bound state ($n=1$).

    Hint: $-13.6$ eV at $n=1$.

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