Week 6 – SS3 Second Term Physics Notes

 WEEK SIX
TOPIC: ENERGY QUANTIZATION
CONTENT

• Energy Quanta
• Energy Level in Atoms
• Kinetic Energy of Emitted Photon

 Bohr suggested that the electron in the atom exist in discrete energy known as quantization which can be removed from one level to the other. Energy in such bodies is emitted in separate or discrete
energy packet called energy quanta
    E =hf
    h = Planck’s constant.
    f = frequency

 ENERGY LEVEL IN AN ATOM
Electrons in atoms are arranged around their nuclei in position known as energy level or electron shell. It requires more energy to remove electrons from the first energy level than to remove electrons from any of the other higher levels. The energy of an electron is given by the relation .
    E = – 1 R
         n²
n = electron quantum number
R = a constant
The minus sign signifies that work must be done on the electron to remove it from the atom.

 ENERGY LEVEL DIAGRAM
E₅ n =5
E₄ n=4
E₃ n=3
E ₂ n =2
E ₁ n =1
E _o             n = 0 (ground state)

 The ground state is the stable state or an atom corresponding to its minimum energy. When an atom is heated with an energetic particle, the atom is excited. An excited state is an allowed state of higher energy when the atom is unstable. One electron volt (IeV) is the energy acquired by an electron in falling freely through a p.d of 1 Volt = 1.6 x 10 -19J.

 During the excitation from lower energy level, the potential energy is converted into Kinetic energy so that the electrons eventually acquire a velocity given by:
    K. E = ½ MV² = eV.
The energy gained by electron = charge x p.d = eV. Therefore, the electron moves from one level to the other according to the relation.
    En – Eo = hf = eV
λ
Worked example
1.    The change in energy level of an electron in an atom is 6.2 x 10 ^-21J. Calculate :
            (a) the frequency of the photon
            (b) the wavelength
(C = 3.0 x 10⁸ ms -1, h = 6.625 x 10 ^-34Js)
∆ E = En-Eo = 6.2 x 10 ^-21J
∆E = hf
f = ∆E = 6.2 x 10^-21
h     6.625 x 10^-34
f = 9.358 x 10 ²Hz
But C = f λ
:. λ = C = 3.0 x 10⁸
f 9.4 x 10¹²

 2.    An atom excited to an energy level E₂ = -12 .42 x 10^-19J falls to a ground level of energy Eo = – 30.3 x 10-19J. Calculate the frequency and the wavelength of the emitted photon.
∆E = E₂– E_o
    = -12.42 x 10^-19 – ( -30.3 x 10^-19J )
= 17.88 x 10^-19J
f = ∆E = 1.788 x 10^-18
h 6.625 x 10^-34
f = 2.698 x 10¹⁵ Hz.

 3.    The ground state of hydrogen is -26.3eV and the second state is -10.3eV. Calculate the wavelength of the radiation if the electron returns to the ground state.
∆E = E₂ – E_O = -10.3EV – (-26.3ev)
            = 16ev
1ev = 1.6 x 10^-19 J
:. 16ev = 16 x 1.6 x 10^-19J
∆E = hf = hc
λ
:.λ = hc = 6.625 x10³⁴ x 3.0 x 10⁸
∆E 16 x 1.6 x 10^-19
     = 1.9875 x 10^-25

1. 25.6 x 10^-18

   λ = 7.76 x 10^-19 m

    4.    If the p.d by which an electron moves is 1.5kv. Calculate the velocity with which the electron moves if the ration of its charge to mass is 1.9 x 10¹¹ c kg^-1 (b) the kinetic energy .
               KE = ½ mv² = ev
                   2ev =mv²
                   v² = 2ev
   m
       But e/m = 1.8 x 10¹¹
           V = √2 x 1.5 x 10³ x 1.8 x 10¹¹
           V = 2.3 x 10⁷m/s
           Ke = eV
           = 1.6 x 10^-19 x 1.5x 10³
               = 2.4 x 10^-16 J.

    GENERAL EVALUATION

   1. With the aid of a diagram, explain charge distribution
   2. Name two devices that can store charge.

    
    READING ASSIGNMENT
   New School physics pgs

    WEEKEND ASSIGNMENT
   1.    When an atom is in ground state, it is said to be (A) excited (B) stable (C) ionized
   2.    In which of the following transitions is the largest quantum of energy liberated by an hydrogen atom, when the electron changes energy level? (A) n=2 to n=1 (B) n=2 to n=3 (C) n=3 to n=2
   (D) n=1 to n=2
   3.    Which of the following give rise to the line spectra obtained from atoms. (A) change of electron from a higher to lower energy level (B) potential energy of the electron inside an atom
       (C ) Excitement of an electron in the atom
   4.    A 50KV is applied across an x-ray tube. Calculate the maximum velocity of the electrons produced. [Me= 9.11X10^-31Kg, e= 1.6X10^-19C] (A) 4.2X10⁸m/s (B) 1.8X10⁸m/s (C) 4.2X10⁵m/s
   (D) 1.8X10⁵m/s
   5.    The nucleon number and the proton number of a neutral atom are 238 and 92 respectively. What is the number of neutrons in the atom? (A) 146 (B) 330 (C) 73 (D) 52.

    THEORY
   1.    An electron of charge 1.6X10^-19C is accelerated in a vacuum from rest at zero volt towards a plate 40KV. Calculate the kinetic energy of the electron
   2.    An electron jumps from one energy level to another in an atom radiating 9.0×10^-19J. If h = 6.6 x 10 ^-34Js and C = 3.0 x 10⁸m/s, what is the wavelength, and the frequency of the radiation.