Structure Of The Atom L-4 Structure of the atom
→ \rightarrow → → \rightarrow → Structure of the atom → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Bohr's model(postulates of bohr)
Electron moves around nucleus in fixed paths (orbits) constant energy (stationary state)
Electron moves from one orbit to another by absorbing or emitting energy
Value of energy
2 → 1 2\rightarrow 1 2 → 1 E 2 − E 1 = Δ E \quad E_2-E_1=\Delta E E 2 − E 1 = Δ E Δ E = h ν \Delta E=h \nu Δ E = h ν ν = E 2 − E 1 h \nu=\frac{E_2-E_1}{h} ν = h E 2 − E 1 λ = c ν = h c E 2 − E 1 \lambda=\frac{c}{\nu}=\frac{h c}{E_2-E_1} λ = ν c = E 2 − E 1 h c ν ˉ = E 2 − E 1 h c \bar{\nu}=\frac{E_2-E_1}{h c} ν ˉ = h c E 2 − E 1
Structure of the atom → \rightarrow → → \rightarrow → Bohr's model(postulates of bohr) → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Bohr's model
Only those orbits are allowed , where angular momentum is constant
m v r = n h 2 π ⏟ n = 1 , 2 , 3 , ⋯ {m v r}=\underbrace{n \frac{h}{2 \pi}}_{n=1,2,3, \cdots} m v r = n = 1 , 2 , 3 , ⋯ n 2 π h m v r = h 2 π , 2 h 2 π , 3 h 2 π … {m v r}=\frac{h}{2 \pi}, \frac{2 h}{2 \pi}, \frac{3 h}{2 \pi} \ldots m v r = 2 π h , 2 π 2 h , 2 π 3 h … P = m v P = m v P = m v L = m v r L = m v r L = m v r
→ \rightarrow → → \rightarrow → Bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Results from bohr's model
The orbits are numbered n = 1,2,3...
Radius of orbit r n = 0.529 n 2 Z A o r_n = 0.529 \frac {n^2}{Z} A^{o} r n = 0.529 Z n 2 A o
Bohr's model(postulates of bohr) → \rightarrow → → \rightarrow → Results from bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Results from bohr's model
For H-atom Z = 1\hspace {1mm}
r 1 = 0.529 A o r_1=0.529 A^{o} r 1 = 0.529 A o r 2 = 2.12 A o r_2=2.12 A^{o} r 2 = 2.12 A o r 3 = 4.76 A o r_3=4.76 A^{o} r 3 = 4.76 A o Applicable to all single electron species - H , H e + , L i 2 + \mathrm{H} , \mathrm{He^+} , \mathrm{Li}^{2+} H , H e + , Li 2 +
Z = 1 2 3 Z =1\quad2\quad 3 Z = 1 2 3
Bohr's model → \rightarrow → → \rightarrow → Results from bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Results from bohr's model
Speed of electron in orbit n
Results from bohr's model → \rightarrow → → \rightarrow → Results from bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Results from Bohr's model
Energy of orbit n
E n = − 2.18 × 10 − 18 ⏟ ( Z 2 n 2 ) J E_n=\underbrace{-2.18\times10^{-18}}\left(\frac{Z^2}{n^2}\right)\mathrm{J} E n = − 2.18 × 1 0 − 18 ( n 2 Z 2 ) J E n E_n E n \quad = − 13.6 ⏟ ( Z 2 n 2 ) e v =\underbrace{-13.6}\left(\frac{Z^2}{n^2}\right) \mathrm{ev} = − 13.6 ( n 2 Z 2 ) ev
R H = 109677 c m − 1 R_H=109677 \mathrm{cm}^{-1} R H = 109677 cm − 1
Results from bohr's model → \rightarrow → → \rightarrow → Results from Bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Results from bohr's model
Results from bohr's model → \rightarrow → → \rightarrow → Results from bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Results from bohr's model
E n = − R H ( Z 2 n 2 ) E_n=-R_H\left(\frac{Z^2}{n^2}\right) E n = − R H ( n 2 Z 2 ) n 2 → n 1 ( n 2 > n 1 ) n_2 \rightarrow n_1 \quad\left(n_2>n_1\right) n 2 → n 1 ( n 2 > n 1 ) E n 2 = − R H ( Z 2 n 2 2 ) E_{n_2}=-R_H\left(\frac{Z^2}{n_2^2}\right) E n 2 = − R H ( n 2 2 Z 2 ) E n 1 = − R H ( Z 2 n 1 2 ) E_{n_1}=-R_H\left(\frac{Z^2}{n_1^2}\right) E n 1 = − R H ( n 1 2 Z 2 ) Δ E = − R H Z 2 ( 1 n 2 2 − 1 n 1 2 ) \Delta E =-R_H Z^2\left(\frac{1}{n_2^2}-\frac{1}{n_1^2}\right) Δ E = − R H Z 2 ( n 2 2 1 − n 1 2 1 ) Δ E = R H Z 2 ( 1 n 1 2 − 1 n 2 2 ) \Delta E=R_H Z^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) Δ E = R H Z 2 ( n 1 2 1 − n 2 2 1 )
Results from Bohr's model → \rightarrow → → \rightarrow → Results from bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Results from bohr's model
Results from bohr's model → \rightarrow → → \rightarrow → Results from bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Limitations of bohr's model
Applicable only for single electronic species H H H H e + He^+ H e + L i 2 + Li^{2+} L i 2 +
Splitting of spectral line in m a g n e t i c f i e l d ⏟ \underbrace {magnetic field} ma g n e t i c f i e l d e l e c t r i c f i e l d ⏟ \underbrace {electric field} e l ec t r i c f i e l d
\quad \quad \quad \quad \quad\quad\quad\quad\quad \quad\quad\quad \quad
Could not describe chemical bond
Results from bohr's model → \rightarrow → → \rightarrow → Limitations of bohr's model → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 De Broglie's hypothesis (1924)
Matter has a wave nature
λ = h p = h m v \lambda = \frac{h}{p} = \frac{h}{m v} λ = p h = m v h
For electron 1st Bohr's orbit
m = 9.1 × 10 − 31 \times 10^{-31} × 1 0 − 31 × 10 6 \times 10^6 × 1 0 6 m s − 1 ms^{-1} m s − 1
λ = 6.626 × 10 − 34 J . s 9.1 × 10 − 31 k g × 2.18 × 10 6 m s − 1 = 0.33 ⏟ n m \lambda = \frac{6.626 \times 10^{-34} \mathrm{J} . \mathrm{s}}{9.1 \times 10^{-31} \mathrm{kg} \times 2.18 \times 10^6 \mathrm{ms}^{-1}}\ {=}\underbrace{0.33} \mathrm{nm} λ = 9.1 × 1 0 − 31 kg × 2.18 × 1 0 6 ms − 1 6.626 × 1 0 − 34 J . s = 0.33 nm Object - 100g = v = 100km/h
λ = 6.626 × 10 − 34 J . s 0.1 k g × 27.5 m s − 1 \lambda = \frac{6.626 \times 10^{-34} \mathrm{J.s}}{0.1 \mathrm{kg} \times 27.5 \mathrm{ms}^{-1}} λ = 0.1 kg × 27.5 ms − 1 6.626 × 1 0 − 34 J.s
= 0.24 × 10 − 33 n m = 0.24 \times 10^{-33} \mathrm{nm} = 0.24 × 1 0 − 33 nm
Results from bohr's model → \rightarrow → → \rightarrow → De Broglie's hypothesis (1924) → \rightarrow → → \rightarrow →
Structure Of The Atom L-4 Thank you
Limitations of bohr's model → \rightarrow → → \rightarrow → Thank you → \rightarrow → → \rightarrow →
Resume presentation
Structure Of The Atom L-4 Structure of the atom $\rightarrow$ $\rightarrow$ Structure of the atom $\rightarrow$ $\rightarrow$ Bohr's model(postulates of bohr)
