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  4. Atoms Chapter-Wise Test 2

Atoms Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What was the primary evidence from Rutherford’s alpha-particle scattering experiment that led to the nuclear model of the atom?

The observation that a small fraction of alpha-particles were deflected by large angles (e.g., more than 90°) indicated a small, dense, positively charged nucleus at the atom’s center.

All alpha-particles passed through undeflected
Some alpha-particles were deflected by large angles
Alpha-particles were absorbed by the foil
Uniform scattering in all directions
1

In Rutherford’s scattering experiment, what does the small number of alpha-particles undergoing head-on collisions suggest?

The rarity of head-on collisions (1 in 8000 rebounding back) suggests that the nucleus, containing most of the mass and charge, is very small compared to the atom.

Nucleus occupies a small volume
Atom is uniformly dense
Electrons cause large deflections
Foil has a large thickness
1

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

\( E_4 = -\frac{13.6}{4^2} = -0.85 \, \text{eV} \), \( E_2 = -3.4 \, \text{eV} \).

\( \Delta E = E_4 - E_2 = -0.85 - (-3.4) = 2.55 \, \text{eV} \).

1.89 eV
10.2 eV
2.55 eV
12.09 eV
3

In Rutherford’s model, what is the ratio of the size of the nucleus to the size of the atom if the nuclear radius is \( 10^{-15} \, \text{m} \) and atomic radius is \( 10^{-10} \, \text{m} \)?

Ratio = \( \frac{\text{nuclear radius}}{\text{atomic radius}} = \frac{10^{-15}}{10^{-10}} = 10^{-5} \).

\( 10^{-5} \)
\( 10^{-4} \)
\( 10^5 \)
\( 10^4 \)
1

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

\( E_5 = -\frac{13.6}{5^2} = -0.544 \, \text{eV} \), \( E_2 = -3.4 \, \text{eV} \).

\( \Delta E = -0.544 - (-3.4) = 2.856 \, \text{eV} \approx 2.86 \, \text{eV} \).

1.89 eV
2.86 eV
10.2 eV
12.09 eV
2

A hydrogen atom in the \( n = 3 \) state emits a photon and returns to the ground state. What is the maximum energy of the photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_3 = -1.51 \, \text{eV} \), \( E_1 = -13.6 \, \text{eV} \).

\( \Delta E = 12.09 \, \text{eV} \).

1.89 eV
2.55 eV
10.2 eV
12.09 eV
4

What is the speed of an electron in the \( n = 3 \) 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 \( n = 3 \): \( v_3 = \frac{2.2 \times 10^6}{3} \approx 7.33 \times 10^5 \, \text{m/s} \).

\( 1.1 \times 10^6 \, \text{m/s} \)
\( 7.33 \times 10^5 \, \text{m/s} \)
\( 2.2 \times 10^6 \, \text{m/s} \)
\( 4.4 \times 10^5 \, \text{m/s} \)
2

What is the angular momentum of an electron in the \( n = 3 \) state of a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \))

\( L = n \frac{h}{2\pi} \).

For \( n = 3 \): \( L = 3 \times \frac{6.6 \times 10^{-34}}{2 \times 3.14} \approx 3.15 \times 10^{-34} \, \text{J·s} \).

\( 1.05 \times 10^{-34} \, \text{J·s} \)
\( 2.1 \times 10^{-34} \, \text{J·s} \)
\( 3.15 \times 10^{-34} \, \text{J·s} \)
\( 4.2 \times 10^{-34} \, \text{J·s} \)
3

What is the frequency of revolution of an electron in the first orbit of a hydrogen atom if its speed is \( 2.2 \times 10^6 \, \text{m/s} \) and radius is \( 5.3 \times 10^{-11} \, \text{m} \)?

\( v = \frac{v}{2\pi r} \).

\( v = \frac{2.2 \times 10^6}{2 \times 3.14 \times 5.3 \times 10^{-11}} \approx 6.6 \times 10^{15} \, \text{Hz} \).

\( 3.3 \times 10^{15} \, \text{Hz} \)
\( 6.6 \times 10^{15} \, \text{Hz} \)
\( 1.1 \times 10^{16} \, \text{Hz} \)
\( 2.2 \times 10^{15} \, \text{Hz} \)
2

What is the minimum energy required to excite a hydrogen atom from its ground state to the first excited state? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_1 = -13.6 \, \text{eV} \), \( E_2 = -3.4 \, \text{eV} \).

\( \Delta E = -3.4 - (-13.6) = 10.2 \, \text{eV} \).

10.2 eV
12.09 eV
13.6 eV
1.89 eV
1

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