The wavelength of light in the visible region is about \(390\;\mathrm{mm}\) for violet colour, about \(550\;\mathrm{mm}\)\((\)average wavelength\()\) for yellow-green color and about \(770\;\mathrm{nm}\) for red colour. What are the energies of photons in \(\;\text{eV}\) at the \((i)\) violet end, \((\mathit{ii})\) average wave length, yellow-green colour, and \((iii)\) red end of the visible spectrum? \(h=6.62\times 10^{-34}\;\text{Js}\) \(e=1.6\times 10^{-19}\;\text{C}\)
Answer
\(\lambda _1=390\;\mathrm{nm}\) \(\lambda _2=550\;\mathrm{nm}\) \(\lambda _3=760\;\mathrm{nm}\) Respectively for violet, yellow-green and red colour. Consider \(E_1,E_2\;\text{ and}\;E_3\) to be their energies respectively. Now by using the following relation \(E=\frac{\text{hc}}{\lambda }\) \(E_1=\frac{\mathit{hc}}{\lambda _1}\) \(=\frac{\left(6.62\times 10^{-34}\times 3\times 10^8\right)}{390\times 10^{-9}}\) \(=5.10\times 10^{-19}\;\text{V}\) \(=\frac{\left(5.10\times 10^{19}\right)}{1.6\times 10^{-19}}=3.19\;\text{eV}\) \(E_2=\frac{\text{hc}}{\lambda _2}\) \(=\frac{\left(6.62\times 10^{-34}\times 3\times 10^8\right)}{550\times 10^{-9}}\) \(=3.62\times 10^{-19}\;\text{V}\) \(=\frac{\left(3.62\times 10^{-19}\right)}{1.6\times 10^{-19}}=3.19\;\text{eV}\) \(E_3=\frac{\mathit{hc}}{\lambda _3}\) \(=\frac{\left(6.62\times 10^{-34}\times 3\times 10^8\right)}{760\times 10^{-9}}\) \(=2.62\times 10^{-19}\;\text{V}\) \(=\frac{\left(2.62\times 10^{-19}\right)}{1.6\times 10^{-19}}=1.64\;\text{eV}\)
Let \( ABCD\) is a unit square and each side of the square is divided in the ratio \( \alpha :\left(1-\alpha \right)\left(0<\alpha <1\right).\) These points are connected to obtain another square. The sides of new square are divided in the ratio \( \alpha :\left(1-\alpha \right)\) and points are joined to obtain another square. The process is continued indefinitely. Let \( {a}_{n}\) denote the length of side and \( {A}_{n}\) the area of \( n\)\(^{th}\) square. The value of \( \alpha \) for which side of \( n\)\(^{th}\) square equal to the diagonal of \( (n+1)\)\(^{th}\) square is ( )
The wavelength of light in the visible region is about \(390\; \mathrm{mm}\) for violet colour, about \(550\; \mathrm{mm}\)\((\)average wavelength\()\) for yellow-green colour and about \(760 \;\mathrm{mm}\) for red colour. From which of the photosensitive materials with work functions listed in table and can you build a photoelectric device that operates with visible light?
Electrolysis of dilute aqueous \(NaCI\) solution was carried out by passing\( 10 mA\) current\(.\) The time required to liberate \(0.01\ mole)\) of \(H_{2}\) gas at the cathode is \((1 F=96500Cmol^{-l})\)( )