Atoms and Nuclei Chapter-Wise Test 4

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In Rutherford’s scattering experiment, what percentage of alpha-particles scatter by more than 1°?

Given: 0.14% of alpha-particles scatter by more than 1°.

Percentage = 0.14%.

1.4%
0.14%
0.014%
14%
2

What is the angular momentum of an electron in the \( n = 2 \) state of a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \))

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

For \( n = 2 \): \( L = 2 \times \frac{6.6 \times 10^{-34}}{2 \times 3.14} \approx 2.1 \times 10^{-34} \, \text{J·s} \).

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

A photon of energy 10.2 eV is absorbed by a hydrogen atom in the ground state. To which energy level does the electron jump? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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

\( E_n = E_1 + 10.2 = -13.6 + 10.2 = -3.4 \, \text{eV} \).

\( -3.4 = -\frac{13.6}{n^2} \Rightarrow n^2 = 4 \Rightarrow n = 2 \).

1
3
2
4
3

In an alpha-particle scattering experiment, a 5.5 MeV alpha-particle approaches a gold nucleus (Z = 79). What is the approximate distance of closest approach? (Take \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 \), \( e = 1.6 \times 10^{-19} \, \text{C} \), 1 MeV = \( 1.6 \times 10^{-13} \, \text{J} \))

Energy conservation: \( K = \frac{2Ze^2}{4\pi\epsilon_0 d} \).

\( d = \frac{2Ze^2}{4\pi\epsilon_0 K} \).

\( K = 5.5 \, \text{MeV} = 5.5 \times 1.6 \times 10^{-13} = 8.8 \times 10^{-13} \, \text{J} \).

\( d = \frac{2 \times 79 \times (1.6 \times 10^{-19})^2 \times 9 \times 10^9}{8.8 \times 10^{-13}} \).

\( d = \frac{158 \times 2.56 \times 10^{-38} \times 9 \times 10^9}{8.8 \times 10^{-13}} \approx 4.13 \times 10^{-14} \, \text{m} \approx 41 \, \text{fm} \).

Rounded to 40 fm for simplicity.

40 fm
45 fm
50 fm
55 fm
1

Why did Rutherford’s nuclear model fail to explain the stability of atoms?

In classical theory, an accelerating electron (in circular orbit) emits radiation, losing energy and spiraling into the nucleus, contradicting atomic stability.

Nucleus was too small
Electrons had no charge
Accelerating electrons emit radiation
Positive charge was uniform
3

What is the orbital period of an electron in the \( n = 2 \) orbit of a hydrogen atom if \( v_1 = 2.2 \times 10^6 \, \text{m/s} \) and \( r_1 = 5.3 \times 10^{-11} \, \text{m} \)?

\( v_2 = \frac{v_1}{2} = 1.1 \times 10^6 \, \text{m/s} \), \( r_2 = 4 \times 5.3 \times 10^{-11} = 2.12 \times 10^{-10} \, \text{m} \).

\( T = \frac{2\pi r_2}{v_2} = \frac{2 \times 3.14 \times 2.12 \times 10^{-10}}{1.1 \times 10^6} \approx 1.21 \times 10^{-15} \, \text{s} \).

\( 1.51 \times 10^{-16} \, \text{s} \)
\( 6.05 \times 10^{-16} \, \text{s} \)
\( 3.02 \times 10^{-16} \, \text{s} \)
\( 1.21 \times 10^{-15} \, \text{s} \)
4

What is the potential energy of an electron in the \( n = 5 \) state of a hydrogen atom? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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

\( U = -2K = -2 \times 0.544 = -1.088 \, \text{eV} \approx -1.09 \, \text{eV} \).

-0.544 eV
-0.85 eV
-1.09 eV
-3.4 eV
3

What does the line spectrum of hydrogen indicate about its atomic structure?

The line spectrum suggests that electrons occupy discrete energy levels, emitting photons of specific wavelengths when transitioning between them.

Continuous energy distribution
Discrete energy levels
Uniform charge distribution
Random electron motion
2

What is the orbital period 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 \( 5.3 \times 10^{-11} \, \text{m} \)?

\( T = \frac{2\pi r}{v} = \frac{2 \times 3.14 \times 5.3 \times 10^{-11}}{2.2 \times 10^6} \approx 1.51 \times 10^{-16} \, \text{s} \).

\( 1.0 \times 10^{-16} \, \text{s} \)
\( 1.2 \times 10^{-16} \, \text{s} \)
\( 1.8 \times 10^{-16} \, \text{s} \)
\( 1.51 \times 10^{-16} \, \text{s} \)
4

Which of the following statements is incorrect about the hydrogen atom’s energy levels in Bohr’s model?

Energy levels are discrete and negative, becoming less negative with increasing \( n \), not positive or continuous as in classical models.

Energy is negative in bound states
Energy levels are discrete
Energy is positive in all orbits
Energy approaches zero as \( n \) increases
3

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