| (Mass of electron \[=9\times {{10}^{-31}}kg,\] |
| Velocity of light\[=3\times {{10}^{8}}m\,{{s}^{-1}},\] |
| Planck?s constant \[=6.626\times {{10}^{-34}}Js,\] |
| Charge of electron\[=1.6\times {{10}^{-19}}Je{{V}^{-1}}\]) |
A) 4.0 eV
B) 2.1 Ev
C) 0.9 eV
D) 3.1 eV
Correct Answer: B
Solution :
Given, \[\lambda =4000\overset{o}{\mathop{\text{A}}}\,\] \[v=6\times {{10}^{5}}\,m\,{{s}^{-1}}\] \[h\upsilon ={{w}_{0}}+\frac{1}{2}m{{v}^{2}}\] [\[{{w}_{0}}=\]work function] \[{{w}_{0}}=h\upsilon -\frac{1}{2}m{{v}^{2}}\] \[=\frac{6.626\times {{10}^{-34}}\times 3\times {{10}^{8}}}{4000\times {{10}^{-10}}}-\frac{1}{2}\times 9\times {{10}^{-31}}\times {{(6\times {{10}^{5}})}^{2}}\]\[=(4.9695-1.62){{10}^{-19}}=3.3495\times {{10}^{-19}}J\] \[{{w}_{0}}=\frac{3.3495\times {{10}^{-19}}}{1.6\times {{10}^{-19}}}eV=2.0934\approx 2.1eV\]
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