Question

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

• A. $4.4 \times 10^{5} \,m / s$
• B. $ 8.8\times 10^{7}\,m/s $
• C. $ 8.8\times 10^{5}\,m/s $
• D. $ 4.4\times 10^{7}\,m/s $

Answer 1

The Correct Option is B

Work function \(W =4 eV =4 \times 1.6 \times 10^{-19} J\) \(=6.4 \times 10^{-19} J\) Wavelength of incident radiation \(\lambda=0.2 \mu m =0.2 \times 10^{-6} m\) Maximum KE of liberated electron \(( KE )_{\max }=\frac{h c}{\lambda}-W\) \(\frac{1}{2} m v_{\max }^{2}=\frac{h c}{\lambda}-W\) \(\frac{1}{2} \times 9.1 \times 10^{-31} v_{\max }^{2}\) \(=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{0.2 \times 10^{-6}}-6.4 \times 10^{-19}\) \(=9.9 \times 10^{-19}-6.4 \times 10^{-19}=3.5 \times 10^{-19}\) \(\therefore v_{\max }=\sqrt{\frac{3.5 \times 10^{-19} \times 2}{9.1 \times 10^{-31}}}=\sqrt{\frac{7}{9.1} \times 10^{12}}\) \(=8.8 \times 10^{5} m / s\)

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.