Atoms and Nuclei Chapter-Wise Test 9

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In Rutherford’s nuclear model, why do most alpha-particles pass through the gold foil without deflection?

Most of the atom is empty space, with the nucleus occupying a very small volume, so most alpha-particles do not encounter the nucleus and pass through undeflected.

Atom is mostly empty space
Nucleus is negatively charged
Electrons deflect alpha-particles
Gold foil is too thin
1

What is the role of the impact parameter in Rutherford’s alpha-particle scattering?

The impact parameter determines the scattering angle; a smaller impact parameter leads to a larger deflection due to closer approach to the nucleus.

Measures the energy of alpha-particles
Determines the scattering angle
Indicates the size of the foil
Controls the speed of alpha-particles
2

An electron beam of 12.0 eV excites a hydrogen atom in the ground state. What is the highest energy level reached? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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

\( E_n = -13.6 + 12.0 = -1.6 \, \text{eV} \).

\( -1.6 = -\frac{13.6}{n^2} \Rightarrow n^2 \approx 8.5 \Rightarrow n = 2 \) (since \( E_2 = -3.4 \, \text{eV} < -1.6 \, \text{eV} \)).

3
4
1
2
4

In the Bohr model, what is the ratio of the radius of the \( n = 5 \) orbit to the \( n = 1 \) orbit?

\( r_n = n^2 r_1 \).

\( r_5 = 25 r_1 \), \( r_1 = r_1 \).

Ratio = \( \frac{r_5}{r_1} = 25 \).

9
16
25
4
3

What is the speed of an electron in the \( n = 4 \) orbit of a hydrogen atom if its speed in \( n = 1 \) is \( 2.2 \times 10^6 \, \text{m/s} \)?

\( v_n = \frac{v_1}{n} \).

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

\( 1.1 \times 10^6 \, \text{m/s} \)
\( 5.5 \times 10^5 \, \text{m/s} \)
\( 7.33 \times 10^5 \, \text{m/s} \)
\( 2.2 \times 10^6 \, \text{m/s} \)
2

What is the energy of a photon emitted when an electron drops from \( n = 5 \) to \( n = 4 \) in a hydrogen atom? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_5 = -0.544 \, \text{eV} \), \( E_4 = -0.85 \, \text{eV} \).

\( \Delta E = -0.544 - (-0.85) = 0.306 \, \text{eV} \approx 0.31 \, \text{eV} \).

0.66 eV
0.31 eV
0.97 eV
2.86 eV
2

The radius of the first orbit in a hydrogen atom is \( 5.3 \times 10^{-11} \, \text{m} \). What is the radius of the fifth orbit?

\( r_n = n^2 r_1 \).

For \( n = 5 \): \( r_5 = 5^2 \times 5.3 \times 10^{-11} = 25 \times 5.3 \times 10^{-11} = 1.325 \times 10^{-9} \, \text{m} \).

\( 1.325 \times 10^{-9} \, \text{m} \)
\( 2.12 \times 10^{-10} \, \text{m} \)
\( 4.77 \times 10^{-10} \, \text{m} \)
\( 8.48 \times 10^{-10} \, \text{m} \)
1

Which of the following statements is incorrect about de Broglie’s explanation of Bohr’s model?

De Broglie’s hypothesis supports quantization by proposing standing waves, not continuous waves, which fit an integer number of wavelengths into the orbit.

Electrons form standing waves in orbits
Circumference is an integer multiple of wavelength
Electrons emit continuous waves
Quantization arises from wave nature
2

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

Total energy \( E = K + U \), where \( K = \frac{e^2}{8\pi\epsilon_0 r} \), \( U = -\frac{e^2}{4\pi\epsilon_0 r} \).

\( E = K - 2K = -K \).

\( E = -13.6 \, \text{eV} = -K \Rightarrow K = 13.6 \, \text{eV} \).

13.6 eV
6.8 eV
-13.6 eV
-6.8 eV
1

What limitation of Bohr’s model prevents it from explaining the spectrum of helium?

Bohr’s model applies only to hydrogenic (single-electron) atoms and cannot account for electron-electron interactions in multi-electron atoms like helium.

Lack of nuclear charge
Inaccurate radius calculation
Inability to handle multi-electron atoms
Absence of energy quantization
3

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