Answer

Verified

55.2k+ views

**Hint:**We all know that to eject an electron from the metal surface, we need a specific amount of energy with a particular frequency and that frequency is called threshold frequency which when provided to the electrons so that they can come out of the surface.

**Complete step by step answer:**

As we all know the that by the Einstein’s photoelectric equation, the energy of the photon is given by:

$E = W + KE$ …… (I)

Here E is the energy of the photon , W is the work potential and KE is the kinetic energy of the photo electrons.

As we all know that by Einstein-Planck's equation:

$E = \dfrac{{hc}}{\lambda }$

Here h is the planck’s constant, c is the speed of light and $\lambda $ is the wavelength of emitted radiation.

We will substitute $E = \dfrac{{hc}}{\lambda }$ in equation (I) to finalise the equation. Hence we will get,

$ \Rightarrow \dfrac{{hc}}{\lambda } = W + KE$ ……. (II)

So for the state 1, we can write the equation (II) as, the subscript 1 tells about state 1.

\[ \Rightarrow \dfrac{{hc}}{\lambda } = W + K{E_1}\] …… (III)

Now since the kinetic energy is doubled , so the equation (II) becomes,

$ \Rightarrow \dfrac{{hc}}{{\lambda '}} = W + 2K{E_1}$ …… (IV)

Now we will divide equation (I) from equation (II) and we will get,

\[

\Rightarrow \dfrac{{\dfrac{{hc}}{\lambda }}}{{\dfrac{{hc}}{{\lambda '}}}} = \dfrac{{W + K{E_1}}}{{W + 2K{E_1}}} \\

\Rightarrow \dfrac{{\lambda '}}{\lambda } = \dfrac{{W + K{E_1}}}{{W + 2K{E_1}}} \\

\therefore \dfrac{{\lambda '}}{\lambda } < 1 \\

\]

Now we can clearly say that, \[\lambda ' < \lambda \]. Therefore, the only option matches is (C). Hence the correct option is (C).

**Note:**As we all know that Einstein produced a very effective model of radiation and told that light consists of a very small number of particles. These are not the matter particles but are the packets of pure energy. Each of the packets are called the quantum of energy and are called photons.

Recently Updated Pages

Why do we see inverted images in a spoon class 10 physics JEE_Main

A farsighted man who has lost his spectacles reads class 10 physics JEE_Main

State whether true or false The outermost layer of class 10 physics JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

A train starts from rest from a station with acceleration class 11 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main