Question

20) What phenomenon was Max Planck able to explain and what new assumption did he use in his explanation?

21) Is the following set of quantum numbers allowed? why or why not? n=4 l =1 ml = 2 ms= 1/ 2

22) Describe the Bohr model of the atom. Why was this revolutionary? What was the main limitation of Bohr's model?

Answer 1

20. Ans:

Max Planck was able to explain the Black body radiation. In order to explain this phenomenon, he proposed that energy of electromagnetic waves is quantised rather than continuous. This means that energy could be gained or lost only in the integral multiple of some smallest unit of energy, i.e.quantum (smallest possible unit of energy).

Mathematically, E = nhf

where n = 1,2,3,4,5 . . . .so on

h is known as Planck's Constant

and h = 6.626 x 10^(-34) J.s

and " f " is the frequency of the electromagnetic wave.

21. Ans:

Given set of quantum numbers is n = 4, l = 1, ml = 2, ms = 1/2

We know that n is the Principal Quantum Number and it can take 1, 2,3,4,5,6 . . . . and so on. In the given set, n = 4 .

" l " is the Azimuthal Quantum Number and it can take the value from 0 (zero) to (n - 1). In the given set, l = 1. It is possible as 1 lies between 0 and 3 i.e.(4 - 1)

We know that " ml " take the value from (-l ) to (+ l ). In the given set, ml = 2 but l =1 . As l = 1, ml can take either ( -1 ), 0 or 1. But it is given that ml = 2 , which is not permitted.

So, the above set of quantum numbers is not allowed.

22. Ans:

Bohr's Model Of An Atom :-

Bohr's Postulates :-

i) Electron revolves around the nucleus ina particular orbit, where it doesn't radiate energy. The particular Orbit is known as " Stationary Orbits ".

In Stationary Orbits, the "Angular Momentum" of the revolving electron is equal to the integral multiple of ( h/(2π) ).

i.e. mvr = ( nh )/(2π) where n = 1,2,3,4,5, . . . . and so on.

m = mass of electron

v = velocity of electron

h is the Planck's Constant and h =6.626 x 10^(-34) J.s .

ii) When an electron migrate from higher energy orbit (E1) to lower energy orbit (E2), the difference of energy radiates in the form of electromagnetic wave as -

E1 - E2 = hv where v is tthe frequency of the electromagnetic wave radiated.

Bohr's theory was the first theory which could able to explain the stability of an atom. It could able explain about the energy of the electron and it's angular momentum in a particular orbit in a better manner. Bohr's theory could able to explain the Emission Spectra of Hydrogen atom.So, this theory became revolutionary.

The main limitations of Bohr's model are as follows

i) It could not able to explain spectra of multi electron species.

ii) It predicts definite orbit of electron and goes against the wave nature is electron.

iii) Bohr's model was against Heisenberg Uncertainty Principle.

iv) Bohr's theory could not able to explain the splitting of spectral line in electric field ( Stark effect) and magnetic field ( Zeeman effect).

v) Bohr's theory could not able to explain about the sub energy levels.