Dual Nature of Radiation and Matter

Topics in this chapter

• Photoelectric Equation and Emission
• Photoelectric Current and Photon Flux
• Photon Energy and Wave-Particle Duality
• De Broglie Matter Waves and Diffraction
• Accelerated Particles and Wavelength Ratios

Cheat sheet

Practice questions

1. Question 1Q-374665

   The work function of a certain metal is $2.0\text{ eV}$. If light of frequency $6.0 \times 10^{14}\text{ Hz}$ is incident on the metal surface, the maximum kinetic energy of the emitted photoelectrons is approximately: (Given Planck's constant $h = 6.63 \times 10^{-34}\text{ J s}$, $1\text{ eV} = 1.6 \times 10^{-19}\text{ J}$)

   1. A.0.48 eV
   2. B.2.48 eV
   3. C.4.48 eV
   4. D.1.00 eV
   See the answer and solution
2. Question 2Q-915ECC

   When the wavelength of incident light on a photosensitive surface is changed from $\lambda_1$ to $\lambda_2$, the stopping potential for photoelectrons changes from $V_1$ to $V_2$. The value of the specific charge ($e/m$) of the electron cannot be determined directly, but the ratio of threshold frequency to work function is independent. Which of the following expressions correctly represents the Planck's constant $h$?

   1. A.$\frac{e(V_1 - V_2)}{c(\lambda_2 - \lambda_1)}$
   2. B.$\frac{e(V_1 - V_2)(\lambda_1 \lambda_2)}{c(\lambda_2 - \lambda_1)}$
   3. C.$\frac{e(V_1 - V_2)(\lambda_2 - \lambda_1)}{c(\lambda_1 \lambda_2)}$
   4. D.$\frac{hc}{e(\lambda_2 - \lambda_1)}$
   See the answer and solution
3. Question 3Q-7C2BB4

   An electron and a proton are accelerated through the same potential difference $V$. What is the ratio of their de Broglie wavelengths ($\lambda_e / \lambda_p$)?

   1. A.$1$
   2. B.$\sqrt{\frac{m_p}{m_e}}$
   3. C.$\sqrt{\frac{m_e}{m_p}}$
   4. D.$\frac{m_p}{m_e}$
   See the answer and solution
4. Question 4Q-83EA83

   The threshold frequency for a metallic surface is $\nu_0$. If light of frequency $2\nu_0$ is incident on this surface, the maximum velocity of photoelectrons is $v_1$. If the frequency of incident light is increased to $5\nu_0$, the maximum velocity of photoelectrons becomes $v_2$. The ratio $v_1 : v_2$ is:

   1. A.$1 : 2$
   2. B.$1 : \sqrt{5}$
   3. C.$1 : 4$
   4. D.$2 : 5$
   See the answer and solution
5. Question 5Q-C1DCDD

   Which of the following graphs correctly represents the variation of maximum kinetic energy ($K_{\text{max}}$) of emitted photoelectrons with the frequency ($\nu$) of incident radiation?

   1. A.A straight line parallel to the frequency axis.
   2. B.A parabola opening upwards.
   3. C.A straight line with a positive slope that intersects the frequency axis at the threshold frequency.
   4. D.A straight line passing through the origin.
   See the answer and solution