All formula of atom class 12
Answers
1. Velocity of electron in nth orbit = vn = 2.165 x 106 Z/n m/s
2. Radius of nth orbit = rn = 0.53 x 10–10 n2/Z m
3. Binding energy of an electron in nth state = En = –13.6 Z2/n2 eV/atom
En = –2.17 × 10–16 Zn2/n2 J/atom = –13.6 Zn2/n2 eV/atom
4. Kinetic energy = KE = 1/2 mv2n = KZe2 / rn
5. Potential energy = PE = –kZe2 / 2rn
6. Total energy of an electron = –En = –kZe2 / 2rn
PE = 2TE ; PE = –2KE ; TE = –KE
7. Binding energy of an electron in nth state
En = –13.6 / n2 Z2 eV
8. Ionisation Energy = – B.E.
I.E. = + 13.6 / n2 Z2 eV
9. Ionisation Potential
Ionisation potential = I.E. / e = 13.6/n2 Z2 V
10. Excitation Energy
The energy taken up by an electron to move from lower energy level to higher energy level. Generally it defined from ground state.
• Ist excitation energy = transition from n1 = 1 to n2 = 2
• IInd excitation energy = transition from n1 = 1 to n2 = 3
• IIIrd excitation energy = transition from n1 = 1 to n2 = 4 and so on …
• The energy level n = 2 is also called as Ist excited state.
• The energy level n = 3 is also called as IInd excited state. & so on …
In general, excitation energy (ΔE) when an electron is excited from a lower state n1 to any higher state n2 is given as:
ΔE = 13.6 Z2 (1/n12 – 1/n22) eV
11. Energy released when an electron jumps from a higher energy level (n2) to a lower energy level (n1) is given as:
ΔE = 13.6 Z2 (1/n12 – 1/n22) eV
If v be the frequency of photon emitted and λ be the wavelength, then:
ΔE =hv = h c/λ
The wavelength (λ) of the light emitted an also be determined by using:
1/λ = v = R Z2 (1/n12 – 1/n22)
R = 1.096 x 107 /m
Important: Also remember the value of 1/R = 911.5 Å for calculation of λ to be used in objectives only).
12. The number of spectral lines when an electron falls from n2 to n1 = 1 (i.e. to the ground state) is given by:
No. of lines = n2(n2–1) / 2
If the electron falls from n2 to n1, then the number of spectral lines is given by:
No. of lines = (n2 – n1 + 1) (n2–n1) / 2
hi
here is your answer
FORMULA OF DISTANCE TO CLOSEST APPROACH
ro = 1 / 4π εo . 2Ze2 / Ek
where, Ek = kinetic energy of the particle.
Bohr Model of atom
mvr = nh / 2π
where n = I, 2. 3,… called principle quantum number.
The radiation of energy occurs only when any electron jumps from one permitted orbit to another permitted orbit.
Energy of emitted photon
hv = E2 – E1
where E1 and E2 are energies of electron in orbits.
Radius of orbit of electron is given by
r = n2h2 / 4π2 mK Ze2 ⇒ r ∝ n2 / Z
where, n = principle quantum number, h = Planck’s constant, m = mass of an electron, K = 1 / 4 π ε, Z = atomic number and e = electronic charge.
Velocity of electron in any orbit is given by
v = 2πKZe2 / nh ⇒ v ∝ Z / n
Frequency of electron in any orbit is given by
v = KZe2 / nhr = 4π2Z2e4mK2 / n3 h3
⇒ v prop; Z3 / n3
Kinetic energy of electron in any orbit is given by
Ek = 2π2me4Z2K2 / n2 h2 = 13.6 Z2 / n2 eV
Potential energy of electron in any orbit is given by
Ep = – 4π2me4Z2K2 / n2 h2 = 27.2 Z2 / n2 eV
⇒ Ep = ∝ Z2 / n2
Total energy of electron in any orbit is given by
E = – 2π2me4Z2K2 / n2 h2 = – 13.6 Z2 / n2 eV
⇒ Ep = ∝ Z2 / n2
THE PICTURES IN ATTACHMENT ARE OF=
1) and 2) are Rutherford scattering formula
3) formula for impact perimeter.
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