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  • Work function of nickel is . When ultraviolet radiation of wavelength <img alt="2000 \AA

Work function of nickel is 5.01 \mathrm{eV}. When ultraviolet radiation of wavelength 2000 \AA is incident on the surface of nickel, electrons are emitted. What will be the maximum velocity of emitted electrons?
 

Option: 1

3 \times 10^8 \mathrm{~ms}^{-1}


Option: 2

6.46 \times 10^5 \mathrm{~ms}^{-1}


Option: 3

10.36 \times 10^5 \mathrm{~ms}^{-1}


Option: 4

8.54 \times 10^6 \mathrm{~ms}^{-1}


Answers (1)


Energy corresponding to 2000 \AA 

\mathrm{E}=\frac{12375}{\lambda}=\frac{12375}{2000} \mathrm{eV}=6.2 \mathrm{eV}

Maximum kinetic energy,

\begin{aligned} & K=h v-h v_0 \\ & K=E-W \\ & =(6.2-5.01) \mathrm{eV} \\ & =1.19 \mathrm{eV}\\ &\text{Now, }\mathrm{k}_{\max }=\frac{1}{2} \mathrm{mv}_{\max }^2\\ & \Rightarrow \frac{1}{2} \times 9.1 \times 10^{-31} \times \mathrm{v}_{\max }^2=1.19 \times 1.6 \times 10^{-19} \\ & \text { or } \mathrm{v}_{\max }^2=\frac{1.19 \times 1.6 \times 10^{-19} \times 2}{9.1 \times 10^{-31}} \\ & \text { or } \mathrm{v}_{\max }^2=0.418 \times 10^{12}=41.8 \times 10^{10} \\ & \text { or } \mathrm{v}_{\max }=6.46 \times 10^5 \mathrm{~m} / \mathrm{s} \end{aligned}

 

Posted by

Kshitij

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