Question

When electromagnetic radiation at wavelength 300nm falls on the surface of sodium, electrons are emitted with a kinetic energy of $1.68\times {{10}^{5}}Jmo{{l}^{-1}}$ . What is the minimum energy needed to remove an electron from sodium?

Answer 1

Hint: The minimum energy required to eject an electron from the surface is called the photoelectric work function. To calculate this energy, we need to keep the given formulas in mind
\[h{{\nu }_{\circ }}=h\nu -K.E.\]
\[h\nu \]\[=\dfrac{h.C}{\lambda }\]
Where h is the planck’s constant, \[\nu \] is the frequency of the wave absorbed, C is the speed of light, K.E. is the kinetic energy of the emitted electron, \[{{\nu }_{\circ }}\] is the threshold frequency and \[\lambda \] is the wavelength of the light.

Complete step by step answer:
We have to find the minimum energy needed to remove an electron from sodium that is threshold energy. The required term is given by the following expression:
\[h{{\nu }_{\circ }}=h\nu -K.E.\]
\[=\dfrac{h.C}{\lambda }-\dfrac{1.68\times {{10}^{5}}/mol}{6.023\times {{10}^{23}}}\]
\[h{{\nu }_{\circ }}=\dfrac{6.626\times {{10}^{-34}}\times 3\times {{10}^{8}}}{300\times {{10}^{-9}}}-\dfrac{1.68\times {{10}^{5}}/mol}{6.023\times {{10}^{23}}}\]
= \[0.06626\times {{10}^{-17}}-0.2789\times {{10}^{-18}}\]
= \[0.06626\times {{10}^{-17}}-0.02789\times {{10}^{-17}}\]
= \[0.03837\times {{10}^{-17}}\] joules.
Hence, the minimum energy needed to remove an electron from sodium is \[0.03837\times {{10}^{-17}}\] joules.

Note: Photoelectric effect is defined as a phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation. Electromagnetic radiation is emitted when an atom absorbs energy. The absorbed energy causes one or more electrons to change their position within the atom. When the electron returns to their original position, an electromagnetic wave is produced. These electrons in these atoms are then in a high energy state as they absorbed the energy.
This photoelectric effect occurs when light above a certain frequency called the threshold frequency is incident on metals, this causes electrons to escape from the metal. The threshold frequency is the minimum frequency of radiation that will produce a photoelectric effect.