Question

a) Explain Aufbau principle in detail. Write the increasing order energy of orbitals upto 5d.
b) A photon of wavelength $4\times {10}^{-7}m$ strikes on metal surface, the work function of the metal being 2.13 eV. Calculate
(i) the energy of photon (eV)
(ii) the kinetic energy of the emission, and
(ii) the velocity of the photoelectron. $(1eV=1.6020\times {10}^{-19}J)$

Answer 1

a) According to aufbau principle "in the ground state of the atoms the orbitals are filled with electrons in order of the increasing energies."

Electrons enter the orbitals according to following $(n+l)$ rules.

1. Orbitals are filled in order of increasing value of $(n+l)$.
2. If two orbitals have same value of $(n+l)$, then the orbital with lower value of n will be filled first.
3. The order of energy of different orbitals in an attorney is given below,. $1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d$

b)

• energy of the photon is given by,
  

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

$E=\frac{(6.63\times {10}^{-34}Js)(3\times {10}^{8}m/s)}{4\times {10}^{-7}m}$

$E=5\times {10}^{-19}J=3.125eV$

• Kinetic energy of the emission is given by,
  

$K.E_{max}=E-W$

Here $W$ is the work function and $E$ is the energy of the photon

$K.E_{max}=3.125eV-2.13eV=1eV$

• $K.E_{max}=\frac{1}{2}m{v}_{max}^2$

$v_{max}^2=\frac{2K.E_{max}}{m}$

$v_{max}=\sqrt{\frac{2(1.6\times {10}^{-19})J}{9.1\times {10}^{-31}kg}}$

$v_{max}=6\times {10}^{5}m/s$