Question

The work function of an element is the energy required to remove an electron from the surface of the solid element. The work function for lithium is $ 279.7kJmo{l^{ - 1}} $ . What is the maximum wavelength of light that can remove an electron from the atom?

Answer 1

Hint: In photoelectric effect, threshold wavelength i.e., wavelength associated with work function is the maximum wavelength of light for which the metal emits electrons. In the question, we need to calculate maximum wavelength for one electron, so we first have to convert the given work function from per mole to per electron and then with the help of Plank-Einstein equation, we will calculate the corresponding wavelength.
Plank-Einstein equation: $ E = \dfrac{{hc}}{\lambda } $
Where, $ E $ is energy, h is the Planck’s constant with numerical value $ 6.626 \times {10^{ - 34}}Js $ , $ c $ is the speed of light i.e., $ 3 \times {10^8}m{s^{ - 1}} $ and $ \lambda $ is the wavelength associated with it.

Complete Step By Step Answer:
We know that work function is the minimum amount of energy i.e., thermodynamic work required to remove an electron from the surface of a solid to a point in the vacuum outside the solid surface. When light strikes on a surface of metal, electrons on the surface get energy from light and get emitted from the surface.
As the energy of one photon is the function of frequency of light. Hence, for emission of photon, a minimum frequency of incident light should be achieved which is known as threshold frequency and we know that wavelength is inversely proportional to frequency, so the minimum frequency will lead to the maximum wavelength of the light which will be required to emit a photon from the surface of metal which is known as threshold wavelength.
Now, as per question, the work function of lithium per mole of an atom is given as $ 279.7kJmo{l^{ - 1}} $ . Because $ 1\;{\text{mole}} = 6.023 \times {10^{23}}{\text{electrons}} $ , so the work function of lithium per electron of atom will be as follows:
  $ {E^o} = \dfrac{{279.7}}{{6.023 \times {{10}^{23}}}} $
 $ \Rightarrow {E^o} = 46.44 \times {10^{ - 23}}kJ $
 $ \Rightarrow {E^o} = 4.64 \times {10^{ - 19}}J $
According to Plank-Einstein equation:
 $ E = \dfrac{{hc}}{\lambda } $
Substituting values:
 $ \Rightarrow 4.64 \times {10^{ - 19}} = \dfrac{{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{\lambda } $
 $ \Rightarrow \lambda = \dfrac{{19.878 \times {{10}^{ - 26}}}}{{4.64 \times {{10}^{ - 19}}}} $
 $ \Rightarrow \lambda = 4.26 \times {10^{ - 7}}m $
Hence, the maximum wavelength of light that can remove an electron from the lithium atom is $ 4.26 \times {10^{ - 7}}m $ .

Note:
Ensure not to get confused between the term photon and electron. An atom absorbs or emits light in discrete packets which are known as photons. Basically, in photoelectric effect electrons absorb energy from incident light in the form of photons and are emitted from metal surfaces known as photoelectrons.