Atoms and Nuclei Chapter-Wise Test 7

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Why does the Bohr model predict discrete spectral lines for hydrogen?

Discrete spectral lines arise because electrons transition between fixed energy levels, emitting photons with energies equal to the differences between these levels.

Continuous electron motion
Uniform charge distribution
Fixed energy level transitions
Random energy emissions
3

In Bohr’s model, what prevents an electron from emitting radiant energy while revolving in a stable orbit?

Bohr’s first postulate states that electrons in certain stable orbits (stationary states) do not emit radiant energy, contrary to classical electromagnetic theory.

Electrons revolve in stationary orbits
Electrons spiral into the nucleus
Electrostatic force cancels radiation
High speed of revolution
1

Which of the following statements is correct about the ionization energy of a hydrogen atom in Bohr’s model?

The ionization energy is the energy required to remove the electron from the ground state (\( n = 1 \), -13.6 eV) to infinity (0 eV), which is 13.6 eV.

It is zero in the ground state
It increases with orbit number
It is negative for all states
It is 13.6 eV from the ground state
4

What is the primary reason Rutherford’s model could not explain the line spectra of atoms?

Rutherford’s model lacks quantized energy levels, predicting continuous radiation as electrons accelerate, not discrete spectral lines.

Nucleus was too small
No quantized energy levels
Electrons had no charge
Positive charge was uniform
2

What is the energy required to ionize a hydrogen atom from its ground state? (Ground state energy = -13.6 eV)

Ionization energy = energy to reach \( E = 0 \) from ground state.

\( E_1 = -13.6 \, \text{eV} \), \( E_\infty = 0 \, \text{eV} \).

Energy required = \( 0 - (-13.6) = 13.6 \, \text{eV} \).

13.6 eV
10.2 eV
3.4 eV
1.51 eV
1

A hydrogen atom in the ground state is bombarded with a 12.5 eV electron beam. What is the maximum energy level the electron can reach? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_1 = -13.6 \, \text{eV} \).

\( E_n = -13.6 + 12.5 = -1.1 \, \text{eV} \).

\( -1.1 = -\frac{13.6}{n^2} \Rightarrow n^2 \approx 12.36 \Rightarrow n = 3 \) (since \( E_3 = -1.51 \, \text{eV} < -1.1 \, \text{eV} \), \( n = 3 \)).

2
4
1
3
4

In Rutherford’s scattering experiment, what does a small fraction of alpha-particles rebounding back indicate?

It indicates that the positive charge and most of the mass are concentrated in a small nucleus, causing strong repulsion in head-on collisions.

Electrons are heavy
Foil is uniformly charged
Atom is mostly solid
Small, dense nucleus exists
4

In a hydrogen atom, the total energy of an electron in the ground state is -13.6 eV. What is the magnitude of its potential energy?

\( E = K + U \), \( K = 13.6 \, \text{eV} \), \( U = -2K = -27.2 \, \text{eV} \).

Magnitude = \( |U| = 27.2 \, \text{eV} \).

27.2 eV
13.6 eV
6.8 eV
3.4 eV
1

What does the presence of discrete wavelengths in the hydrogen spectrum indicate?

Discrete wavelengths indicate that electrons transition between specific energy levels, emitting or absorbing photons of fixed energies.

Electrons occupy fixed energy levels
Electrons move randomly in the atom
Nucleus emits continuous radiation
Atom has a uniform charge distribution
1

In Rutherford’s experiment, what does the scattering of alpha-particles at small angles indicate?

Small-angle scattering occurs when alpha-particles pass far from the nucleus (large impact parameter), experiencing weak repulsion.

Nucleus is uniformly charged
Alpha-particles pass far from the nucleus
Electrons cause significant deflection
Foil absorbs most particles
2

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