A) \[2900\,\,\overset{\circ }{\mathop{\text{A}}}\,\]
B) \[2500\,\,\overset{\circ }{\mathop{\text{A}}}\,\]
C) \[5380\,\,\overset{\circ }{\mathop{\text{A}}}\,\]
D) \[1200\,\,\overset{\circ }{\mathop{\text{A}}}\,\]
Correct Answer: C
Solution :
The minimum frequency \[\left( \mu \right)\] of light which can emit photo electrons from a material is called the threshold frequency of that material and the corresponding wavelength is called threshold wavelength\[\left( \lambda \right)\] \[\therefore \] \[E=W=\frac{hc}{\lambda }\] Where \[h\] is Planck?s constant and \[c\] is speed of light. Given, \[E=2.3\,eV=2.3\times 1.6\times {{10}^{-19\,}}\,J\]\[\therefore \,2.3\times 1.6\times {{10}^{-19}}=\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}{\lambda }\] \[\Rightarrow \] \[\lambda =\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}{2.3\times 1.6\times {{10}^{-19}}}\] \[=5380\times {{10}^{-10\,}}\,m\] \[\Rightarrow \] \[\lambda =5380\,\,\overset{\circ }{\mathop{A}}\,\] Note: If wavelength of incident light is greater than\[5380\,\,\overset{\circ }{\mathop{A}}\,\], then no photoelectrons are emitted.
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