Atoms and Nuclei Chapter-Wise Test 8

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the frequency of a photon emitted when an electron drops from \( n = 2 \) to \( n = 1 \) in a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \), 1 eV = \( 1.6 \times 10^{-19} \, \text{J} \))

\( \Delta E = 10.2 \, \text{eV} = 1.632 \times 10^{-18} \, \text{J} \).

\( \nu = \frac{\Delta E}{h} = \frac{1.632 \times 10^{-18}}{6.6 \times 10^{-34}} \approx 2.47 \times 10^{15} \, \text{Hz} \).

\( 6.6 \times 10^{15} \, \text{Hz} \)
\( 1.51 \times 10^{15} \, \text{Hz} \)
\( 2.47 \times 10^{15} \, \text{Hz} \)
\( 4.4 \times 10^{15} \, \text{Hz} \)
3

In Rutherford’s scattering experiment, what causes the large deflection of some alpha-particles?

Large deflections occur due to the strong repulsive force from the positively charged nucleus when alpha-particles approach it closely.

Interaction with electrons
Repulsion by the nucleus
Absorption by the foil
Magnetic field effects
2

What is a limitation of Bohr’s model when applied to the hydrogen atom’s spectrum?

Bohr’s model cannot explain the relative intensities of spectral lines, as it does not account for transition probabilities.

Predicts nuclear size
Fails to quantize energy
Cannot explain line intensities
Applies to all atoms
3

Which of the following statements is correct about the absorption process in a hydrogen atom?

Absorption occurs when an electron jumps to a higher energy level by absorbing a photon matching the energy difference between levels.

Photon is emitted during absorption
Electron remains in the same orbit
Continuous energy is absorbed
Electron jumps to a higher energy level
4

What is the frequency of a photon emitted when an electron drops from \( n = 3 \) to \( n = 1 \) in a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \), 1 eV = \( 1.6 \times 10^{-19} \, \text{J} \))

\( \Delta E = 12.09 \, \text{eV} = 1.9344 \times 10^{-18} \, \text{J} \).

\( \nu = \frac{\Delta E}{h} = \frac{1.9344 \times 10^{-18}}{6.6 \times 10^{-34}} \approx 2.93 \times 10^{15} \, \text{Hz} \).

\( 6.6 \times 10^{15} \, \text{Hz} \)
\( 1.51 \times 10^{15} \, \text{Hz} \)
\( 2.93 \times 10^{15} \, \text{Hz} \)
\( 4.4 \times 10^{15} \, \text{Hz} \)
3

In Bohr’s model, what happens to the energy required to ionize a hydrogen atom as the electron’s orbit number increases?

As \( n \) increases, the energy becomes less negative (closer to zero), so less energy is required to ionize the atom from higher orbits.

Increases
Remains constant
Becomes infinite
Decreases
4

In a hydrogen atom, the total energy of an electron in the \( n = 3 \) state is -1.51 eV. What is its potential energy?

\( E = K + U \), \( K = -E = 1.51 \, \text{eV} \).

\( U = -2K = -2 \times 1.51 = -3.02 \, \text{eV} \).

-3.02 eV
-1.51 eV
1.51 eV
3.02 eV
1

What is the orbital period of an electron in the \( n = 4 \) orbit if \( v_1 = 2.2 \times 10^6 \, \text{m/s} \) and \( r_1 = 5.3 \times 10^{-11} \, \text{m} \)?

\( v_4 = \frac{2.2 \times 10^6}{4} = 5.5 \times 10^5 \, \text{m/s} \).

\( r_4 = 16 \times 5.3 \times 10^{-11} = 8.48 \times 10^{-10} \, \text{m} \).

\( T = \frac{2\pi r_4}{v_4} = \frac{2 \times 3.14 \times 8.48 \times 10^{-10}}{5.5 \times 10^5} \approx 9.68 \times 10^{-15} \, \text{s} \).

\( 1.21 \times 10^{-15} \, \text{s} \)
\( 4.09 \times 10^{-15} \, \text{s} \)
\( 6.05 \times 10^{-16} \, \text{s} \)
\( 9.68 \times 10^{-15} \, \text{s} \)
4

What assumption in Rutherford’s model contradicts classical electromagnetic theory?

Rutherford assumes electrons orbit the nucleus like planets, but classical theory predicts they would radiate energy and collapse, not remain stable.

Nucleus is small
Atom is mostly empty
Electrons orbit without radiating
Positive charge is concentrated
3

In the Bohr model, how many de Broglie wavelengths fit into the circumference of the \( n = 3 \) orbit?

\( 2\pi r_n = n\lambda \).

For \( n = 3 \), number of wavelengths = 3.

2
4
5
3
4

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