Question

describe the main features of the bohr's model of atoms draw a neat and labelled drive gram of energy​

Answer 1

$\bf{BOHR'S \: ATOMIC \: MODEL}$

★ Some key points

1. Atom has centre called nucleus.

2. electron revolves only in fixed circular orbits with fixed energy and fixed velocity.

3. Quantization condition :- electrons revolve only in those circular orbits for which the angular momentum (L) is integral Multiple of h/2π .

→ L = nh/2π = n = integer

n = shell number

→ n = 1 → K

→ n = 2 → L

→ n = 3 → M

→ n = 4 → N

→ Angular momentum = mvr sin∅

→ ∅ = 90° = L = mvr

As mentioned above

→ L = nh/2π

→ mvr = nh/2π ( Bohr's Quantization condition)

h = plank's constant

h = 6.636 × 10^-34 JS

4. while revolving the electrostatic force between electron and nucleus provides centripetal force.

→ Fe = Fc

→ Fe = Kq1q2/r²

→ charge on nucleus = +ze

→ Fc = mv²/r

k = constant ( 1/4πE0)

F = 1/4πE0 eze/r² = mv²/r

5. while revolving in a particular orbit electrons neither gains energy not losses energy.

→ energy of an orbit is fixed

shells → stationary energy level.

By using following equations we can calculate the radius ( r ) , velocity ( v) , kinetic energy (K.E) , potential energy (P.E) and total energy (T.E) of electron.

→ r = n²h²E0/πmze²

→ v = ze²/2hE0

→ K.E = (me⁴/ 8h²E0² ) × z²/n²

→ P.E = -2 (me⁴/ 8h²E0² ) × z²/n²

→ T.E = P.E + K.E

6. electron can accept energy and loose energy .

→ If an electron accepts energy it jumps to higher energy level → excitation of electron

→If electron loses energy it receds to lower energy level → deexcitation of electron

→ An electron gains or loses only those energy which are equal to difference in two energy levels.

→ E1 + ∆E = E2

→ E1 + ∆ E = E3

Now coming to the drawbacks

1. Bohr's model is valid for only single electron specie. ex - H , He+ etc.

2. Bohr considered electron as a moving particle

which later De - broglie gave his hypothesis that every microscopic moving particle is a wave , whose wavelength is given by

$\lambda \: = \frac{h}{mv}$

3. Bohr measured position of electron and velocity of electron .

but according to the Heisenberg uncertainty principle - The exact and simultaneous determination of position and momentum of a moving microscopic particle is impossible.

∆P • ∆x = h/4π

∆P = momentum measure error

∆x = position measure error

4. Spectral lines , they show splitting in magnetic and electric field ( Zeeman and stark effect)

5. Ultra fine spectrum

Solution of E . Schodinger wave equation gives variables . → represent position of electron → those positions whose probability of finding electron is maximum