Question

The work function of a metal is $2 \mathrm{eV}$. If a radiation of wavelength $3000 \dot{\mathcal{A}}$ is incident on it, the maximum kinetic energy of the emitted photoelectrons is:
(Planck's constant $h=6.6 \times 10^{-34} \mathrm{J} \mathrm{s} ;$ Velocity of light $c=3\times {{10}^{8}}m/s;1eV=1.6\times {{10}^{-19}}J$)
(A) $4.4 \times 10^{-19} \mathrm{J}$
(B) $5.6 \times 10^{-19} \mathrm{J}$
(C) $3.4 \times 10^{-19} \mathrm{J}$
(D) $2.5 \times 10^{-19} \mathrm{J}$

Answer 1

We know that radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability. Because the nucleus experiences the intense conflict between the two strongest forces in nature, it should not be surprising that there are many nuclear isotopes which are unstable and emit some kind of radiation. Instability of an atom's nucleus may result from an excess of either neutrons or protons. A radioactive atom will attempt to reach stability by ejecting nucleons (protons or neutrons), as well as other particles, or by releasing energy in other forms. Artificial radioactive isotopes are formed when an atom is bombed with an accelerator or exposing it to slow moving neutrons in a nuclear reactor. Radioactive isotope of carbon is formed when a nitrogen is bombed with slow moving neutrons in a nuclear reactor. It is mostly used as a radioactive indicator.

Complete step by step answer
We know that in solid-state physics, the work function is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. The work function (WF) of a metal can be defined as the minimum energy required to extract one electron from a metal. Obviously the WF is one of the fundamental electronic properties of bare and coated metallic surfaces.
So, any particle that is gravitationally or electrically bound has negative potential energy, i.e. it requires positive work to be added, in order to free it. The negative work function tells you how much work needs to be added to the bound electron, by the photon it absorbs. The binding energy is the work function.
We know that the energy of incident radiation is $\text{E}=\dfrac{\text{hc}}{\lambda }$.
Now we have to put the values in the above expression to get: $\dfrac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{3 \times 10^{-7}}$
After the evaluation we get that: $6.6 \times 10^{-19} \mathrm{J}$
Also, work function is $\phi=2 \times 1.6 \times 10^{-19} \mathrm{J}=3.2 \times 10^{-19} \mathrm{J}$
Hence, maximum kinetic energy of emitted photo electrons will be $6.6 \times 10^{-19} \mathrm{J}-3.2 \times 10^{-19} \mathrm{J}=3.4 \times 10^{-19} \mathrm{J}$

So, the correct answer is option C.

Note: We know that alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produced in other ways. Ionizing radiation comes in three flavours: alpha particles, beta particles and gamma rays. Alpha particles are the least dangerous in terms of external exposure. Each particle contains a pair of neutrons and a pair of protons. Beta particles are electrons that move very quickly that is, with a lot of energy. We know that beta particles can be used to treat health conditions such as eye and bone cancer and are also used as tracers. Strontium-90 is the material most commonly used to produce beta particles. Beta particles are also used in quality control to test the thickness of an item, such as paper, coming through a system of rollers. They travel farther in air than alpha particles, but can be stopped by a layer of clothing or by a thin layer of a substance such as aluminium. Some beta particles are capable of penetrating the skin and causing damage such as skin burns. Alpha particles carry a positive charge, beta particles carry a negative charge, and gamma rays are neutral. Alpha particles have greater mass than beta particles. Gamma rays can only be reduced by much more substantial mass, such as a very thick layer of lead.