Two identical metal plates show photoelectric effect by a light of wavelength \[{\lambda _1}\] on plate \[1\] and \[{\lambda _2}\] on plate \[2\] (Where\[{\lambda _1} = 2{\lambda _2}\] the maximum kinetic energy will be:
\[\left( {\text{A}} \right){\text{ }}2{K_2} = {K_1}\]
\[\left( {\text{B}} \right){\text{ }}{K_{1,}} < \dfrac{{{K_2}}}{2}\]
\[\left( {\text{C}} \right){\text{ }}{K_1} > \dfrac{{{K_2}}}{2}\]
\[\left( {\text{D}} \right){\text{ }}2K - 1 = {K_2}\]

Hint: Out of given particles, an electron has the lowest mass. Therefore, the electron has the maximum kinetic energy. Kinetic power is the strength of mass in motion. The kinetic electricity of an object is the power it has because of its motion.
Kinetic power, the shape of electricity that an object or a particle has via the purpose of its motion. If work, which transfers strength, is done on an object with the aid of making use of a net force, the object speeds up and thereby profits kinetic energy.
Electrical electricity is because of transferring electric powered fees referred to as electrons.
The quicker the prices move, the more electrical strength they bring. As the charges that cause the power are shifting, electric strength is the shape of kinetic power.

Formula used:
\[{E_k} = \dfrac{1}{2}m{v^2}\]
\[{E_k} = \] Kinetic energy of object
\[m = \]Mass of the object
\[v = \]Velocity of the object

Complete step by step answer:
Maximum kinetic energy \[K = \dfrac{{hc}}{\lambda } - \varphi \]
Where \[\lambda \] is the wavelength of incident light and \[\varphi \]is the work function of a metal.
For first case: \[\lambda = {\lambda _1} = 2{\lambda _2}\]
For second case: \[\lambda = {\lambda _2}\]
\[{K_2} = \dfrac{{hc}}{{{\lambda _2}}} - \varphi \]
\[\Rightarrow \dfrac{{{K_2}}}{2} = \dfrac{{hc}}{{{\lambda _2}}} - \varphi \]
From \[(2) - (1)\]we get,
\[\dfrac{{{K_2}}}{2} - {K_1} = \dfrac{\varphi }{2}\]
\[ \Rightarrow \dfrac{{{K_2}}}{2} > {K_1}\]

Hence the correct option is B.

Note: Kinetic Electricity is an asset of a moving object or particle and depends no longer handiest on its motion however additionally on its mass.
The type of motion may be a translation (or movement along a path from one vicinity to some other), rotation approximately an axis, vibration, or any mixture of motions.
Perhaps the most critical asset of kinetic power is its capacity to do work. Work is defined as force performing on an object in the direction of movement. Work and power are so closely related as to be interchangeable.