We know that mass number of the element,
A = p + n = 81    .....(i)
Let the number of protons, p = x
Then, number of neutrons,
\(n=x+\frac { 31.7 }{ 100 } x=1.317x\)
(As number of neutrons are 31.7% more than the protons.)
Hence, from Eq.(i)
\(x+1.317x=81\)
or \(2.317x=81=\frac { 81 }{ 2.317 } =34.958\approx 35\)
Therefore, number of protons = 35 and the symbol is. \(_{ 35 }^{ 81 }{ Br }\) (Number of protons = atomic number)

a) 4d = 4 + 2 = 6, 4f = 4 + 3 = 7, 5s = 5 + 0 = 5, 7p = 7 + 1 = 8
Hence, 5s has the lowest energy.
b) 5p = 5 + 1 = 6, 5d = 5 + 2 = 7, 5f = 5 + 3, 6s = 6 + 0 = 6, 6p = 6  + 1 = 7
Hence, 5f has highest energy.

a) (n + 1) values are
1s = 1 + 0 = 1, 2s = 2+ 0 = 2, 3s = 3 + 0 = 3, 2p = 2 + 1 = 3
Hence, increasing order of their energy is 1s < 2s < 2p < 3s.
b) 4s = 4 + 0 =4, 3s = 3 + 0 = 3, 3p = 3 + 1 = 4, 4d = 4 + 2 = 6.
Hence 3s < 3p < 4s < 4d.
c) 5p = 5 + 1 = 6, 4d = 4 + 2 = 6, 5d = 5 + 2 = 7, 4f = 4 + 3 = 7, 6s = 6 + 0 = 6.
Hence, 4d < 5p < 6s < 4f < 5d.
d) 5f = 5 + 3 = 8, 6d = 6 + 2 = 8, 7s = 7 + 0 = 7, 7p = 7 + 1 = 8.
Hence, 7s < 5f < 6d < 7p.

In Bohr model, an electron is regarded as a charged particle moving in well defined circular orbits about the nucleus. An orbit can completely be defined only if both the position and the velocity of the electron are known exactly at the same time. This is not possible according to the Heisenberg uncertainty principle. Further more, the wave character of the electron is not considered in Bohr model.
Therefore, concept of movement of an electron in an orbit was replaced by the concept of probability of finding electron in an orbital due to de-Broglie concept of dual nature of electron and Heisenberg's uncertainty principle. the changed model is called quantum mechanical model of the atom.

Given, m = 100g = 0.1kg
v = 100km/h = \(\frac { 100\times 1000 }{ 60\times 60 } =\frac { 1000 }{ 36 } { ms }^{ -1 }\)   
From de-Broglie equation, wavelength,
\(\lambda =\frac { h }{ mv } =\frac { 6.626\times { 10 }^{ -34 }{ kgm }^{ 2 }{ s }^{ -1 } }{ 0.1kg\times \frac { 100 }{ 36 } { ms }^{ -1 } } =238.5\times { 10 }^{ -36 }m\)
As the wavelength is very small so wave nature cannot be detected.