Question 1

Q1: Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson's model is ......... the ato...

Accepted Answer

(a) The size of the atom in Thomson's model is no different from the atomic size in Rutherford's model. Both models estimated the atomic radius to be about 10⁻¹⁰ m. (b) In the ground state of Thomson's model electrons are in stable equilibrium, while in Rutherford's model electrons always experience...

Question 2

Q2: Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hyd...

Accepted Answer

If the alpha-particle scattering experiment is repeated with a thin sheet of solid hydrogen, the results would be significantly different from the experiment with the gold foil. 1.  Mass Comparison: A hydrogen nucleus is a single proton, which has a mass of approximately 1.67 × 10⁻²⁷ kg. An alpha pa...

Question 3

Q3: A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upp...

Accepted Answer

According to Bohr's third postulate, when an atom makes a transition from a higher energy level to a lower energy level, it emits a photon with energy equal to the difference between the two levels. Given:    Energy difference, ΔE = 2.3 eV First, we convert the energy from electron volts (eV) to jou...

Question 4

Q4: The ground state energy of hydrogen atom is -13.6 eV . What are the kinetic and potential energies of the electron in this state?

Accepted Answer

For an electron in a hydrogen atom, the total energy (E) is the sum of its kinetic energy (K) and potential energy (U). Given:    Total energy in the ground state, E = -13.6 eV From the analysis of electron orbits in the Rutherford model (which is also used in the Bohr model), we have the following...

Question 5

Q5: A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n=4 level. Determine the wavelength and frequency of photon.

Accepted Answer

The energy of the absorbed photon must be equal to the energy difference between the final state (n = 4) and the initial state (n = 1). The energy of an electron in the n-th level of a hydrogen atom is given by:    Eₙ = -13.6 / n² eV 1.  Calculate the energy of the initial and final states:        I...

Question 6

Q6: (a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the n=1, 2, and 3 levels. (b) Calculate the orbital period in eac...

Accepted Answer

(a) Speed of the electron From Bohr's model, the speed of an electron in the n-th orbit of a hydrogen atom is given by: vₙ = e² / (2nε₀h) Substituting the values of the constants: e = 1.6 × 10⁻¹⁹ C, ε₀ = 8.85 × 10⁻¹² C²/Nm², h = 6.63 × 10⁻³⁴ J s vₙ = (1.6 × 10⁻¹⁹)² / (2n × 8.85 × 10⁻¹² × 6.63 × 10⁻³...

Question 7

Q7: The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10⁻¹¹ m. What are the radii of the n=2 and n=3 orbits?

Accepted Answer

According to Bohr's model for the hydrogen atom, the radius of the n-th stationary orbit is directly proportional to the square of the principal quantum number (n). The formula for the radius is:    rₙ = n²  r₁ Where:    rₙ is the radius of the n-th orbit.    n is the principal quantum number.    r₁...

Question 8

Q8: A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

Accepted Answer

At room temperature, hydrogen atoms are in their ground state (n=1), which has an energy of E₁ = -13.6 eV. The bombarding electrons have a kinetic energy of 12.5 eV. A hydrogen atom can be excited to a higher energy level if it absorbs an amount of energy from a colliding electron that is exactly eq...

Question 9

Q9: In accordance with the Bohr's model, find the quantum number that characterises the earth's revolution around the sun in an orbit of radius 1.5 × 10¹¹...

Accepted Answer

According to Bohr's second postulate (the quantization condition), the angular momentum (L) of an orbiting body is an integral multiple of h/2π.    L = mvr = n  (h / 2π) Where:    m is the mass of the orbiting body (Earth).    v is its orbital speed.    r is the radius of the orbit.    h is Planck's...

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