Solveeit Logo
Login

Question

Physics Question on Photoelectric Effect

If a surface has a work function 4.0 eV4.0 \,eV, what is the maximum velocity of electrons liberated from the surface when it is irradiated with ultraviolet radiation of wavelength 0.2 μm0.2\, \mu m ?

A

4.4×105 m/s4.4 \times 10^{5} \,m / s

B

8.8×107 m/s8.8\times 10^{7}\,m/s

C

8.8×105 m/s8.8\times 10^{5}\,m/s

D

4.4×107 m/s4.4\times 10^{7}\,m/s

Answer

8.8×107 m/s8.8\times 10^{7}\,m/s

Explanation

Solution

Work function W=4eV=4×1.6×10−19JW =4 eV =4 \times 1.6 \times 10^{-19} J =6.4×10−19J=6.4 \times 10^{-19} J Wavelength of incident radiation λ=0.2μm=0.2×10−6m\lambda=0.2 \mu m =0.2 \times 10^{-6} m Maximum KE of liberated electron (KE)max⁡=hcλ−W( KE )_{\max }=\frac{h c}{\lambda}-W 12mvmax⁡2=hcλ−W\frac{1}{2} m v_{\max }^{2}=\frac{h c}{\lambda}-W 12×9.1×10−31vmax⁡2\frac{1}{2} \times 9.1 \times 10^{-31} v_{\max }^{2} =6.6×10−34×3×1080.2×10−6−6.4×10−19=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{0.2 \times 10^{-6}}-6.4 \times 10^{-19} =9.9×10−19−6.4×10−19=3.5×10−19=9.9 \times 10^{-19}-6.4 \times 10^{-19}=3.5 \times 10^{-19} ∴vmax⁡=3.5×10−19×29.1×10−31=79.1×1012\therefore v_{\max }=\sqrt{\frac{3.5 \times 10^{-19} \times 2}{9.1 \times 10^{-31}}}=\sqrt{\frac{7}{9.1} \times 10^{12}} =8.8×105m/s=8.8 \times 10^{5} m / s

The Photoelectric Effect is a phenomena in which an electron is emitted from a metallic surface when a beam of light touches it. Photoelectrons are the electrons that are released from the surface.

  • Photoelectric current is the term used to describe the current generated by photoelectrons.
  • The photoelectric effect is caused, in part, by the energy of light being absorbed by the electrons on the metal surface.
  • The forces holding the electrons to the metal nuclei are overcome by the electrons using this light energy.
  • Heinrich Rudolf Hertz, a German scientist, made the discovery of the photoelectric effect in 1887.
  • He discovered that UV illumination of the emitter plate promoted high-voltage sparks over the detector loop.
  • He came to the conclusion that light aided in some electron emission as a result of this discovery.
  • This led scientists to the conclusion that when the right kind of radiation strikes a metal surface, certain electrons nearby can absorb enough energy from the radiation to repel the positive ions that are attracted to the surface of the material.
  • In 1988, Wilhelm Hallwachs made the observation that the divergence of gold leaf is reduced by ultraviolet light shining on a negatively charged zinc plate linked to an electroscope.
  • He came to the conclusion that a negatively charged zinc plate releases negatively charged particles when exposed to ultraviolet light.
  • The photoelectrons that are released are caused by the action of light.