A) the work function of A is \[3.40\text{ }eV\]
B) the work function of B is \[6.75\text{ }eV\]
C) \[{{T}_{A}}=2.00\,eV\]
D) \[{{T}_{B}}=2.75\,eV\]
Correct Answer: C
Solution :
| \[{{K}_{\max }}=E-{{W}_{0}}\] |
| \[\therefore \,\,{{T}_{A}}=4.25-{{({{W}_{0}})}_{A}}\] |
| \[{{T}_{B}}=({{T}_{A}}-1.5)=4.70-{{({{W}_{0}})}_{B}}\] |
| Equation (i) and (ii) gives \[{{({{W}_{0}})}_{B}}-{{({{W}_{0}})}_{A}}=1.95\,eV\] |
| De Broglie wave length \[\lambda =\frac{h}{\sqrt{2mK}}\Rightarrow \lambda \propto \frac{1}{\sqrt{K}}\] |
| \[\Rightarrow \,\,\frac{{{\lambda }_{B}}}{{{\lambda }_{A}}}=\sqrt{\frac{{{K}_{A}}}{{{K}_{B}}}}\Rightarrow \,2=\sqrt{\frac{{{T}_{A}}}{{{T}_{B}}-1.5}}\Rightarrow {{T}_{A}}=2eV\] |
| From equation (i) and (ii) |
| \[{{W}_{A}}=2.25\,eV\] and \[{{W}_{B}}=4.20\,eV\] |
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