Atoms Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The kinetic energy of an alpha-particle is 7.7 MeV. If it approaches a nucleus with atomic number 79, what is its distance of closest approach? (Use constants: \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 \), \( e = 1.6 \times 10^{-19} \, \text{C} \), 1 MeV = \( 1.6 \times 10^{-13} \, \text{J} \))

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

\( K = 7.7 \times 1.6 \times 10^{-13} = 1.232 \times 10^{-12} \, \text{J} \).

\( d = \frac{2 \times 79 \times (1.6 \times 10^{-19})^2 \times 9 \times 10^9}{1.232 \times 10^{-12}} \).

\( d = \frac{3.641 \times 10^{-28}}{1.232 \times 10^{-12}} \approx 2.95 \times 10^{-14} \, \text{m} \approx 30 \, \text{fm} \).

30 fm

35 fm

40 fm

45 fm

What is the speed of an electron in the \( n = 5 \) 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 \( n = 5 \): \( v_5 = \frac{2.2 \times 10^6}{5} = 4.4 \times 10^5 \, \text{m/s} \).

\( 5.5 \times 10^5 \, \text{m/s} \)

\( 4.4 \times 10^5 \, \text{m/s} \)

\( 7.33 \times 10^5 \, \text{m/s} \)

\( 1.1 \times 10^6 \, \text{m/s} \)

In the Bohr model, what is the ratio of the kinetic energy of an electron in the \( n = 2 \) state to that in the \( n = 1 \) state?

\( K = \frac{e^2}{8\pi\epsilon_0 r} \), \( r_n \propto n^2 \).

\( K_n \propto \frac{1}{n^2} \).

Ratio = \( \frac{K_2}{K_1} = \frac{1/2^2}{1/1^2} = \frac{1}{4} \).

0.5

0.25

An electron in a hydrogen atom has a total energy of -3.4 eV. What is its kinetic energy?

\( E = -K \), \( K = -E = -(-3.4) = 3.4 \, \text{eV} \).

3.4 eV

6.8 eV

1.7 eV

13.6 eV

Which of the following statements is incorrect about Thomson’s model?

Thomson’s model does not include a nucleus; it proposes a uniform positive charge distribution, unlike Rutherford’s nuclear model.

Positive charge is uniform

Electrons are embedded in positive charge

Atom has a small nucleus

Described as a plum pudding model

In the Bohr model, how many de Broglie wavelengths fit into the circumference of the \( n = 5 \) orbit?

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

For \( n = 5 \), number of wavelengths = 5.

What does the absorption spectrum of a hydrogen atom reveal?

The absorption spectrum shows dark lines at wavelengths where photons are absorbed, matching the emission line wavelengths, indicating specific energy level transitions.

Continuous energy emission

Bright lines on a dark background

Random energy levels

Dark lines in a continuous spectrum

What is the kinetic energy of an electron in the \( n = 4 \) state of a hydrogen atom? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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

0.85 eV

1.51 eV

3.4 eV

0.544 eV

What is the orbital period of an electron in the \( n = 3 \) orbit if \( v_1 = 2.2 \times 10^6 \, \text{m/s} \) and \( r_1 = 5.3 \times 10^{-11} \, \text{m} \)?

\( v_3 = \frac{2.2 \times 10^6}{3} \approx 7.33 \times 10^5 \, \text{m/s} \).

\( r_3 = 9 \times 5.3 \times 10^{-11} = 4.77 \times 10^{-10} \, \text{m} \).

\( T = \frac{2\pi r_3}{v_3} = \frac{2 \times 3.14 \times 4.77 \times 10^{-10}}{7.33 \times 10^5} \approx 4.09 \times 10^{-15} \, \text{s} \).

\( 1.51 \times 10^{-16} \, \text{s} \)

\( 1.21 \times 10^{-15} \, \text{s} \)

\( 6.05 \times 10^{-16} \, \text{s} \)

\( 4.09 \times 10^{-15} \, \text{s} \)

What is the energy difference between the \( n = 4 \) and \( n = 2 \) states in a hydrogen atom? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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

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

1.89 eV

2.55 eV

0.66 eV

12.75 eV

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Atoms Chapter-Wise Test 1

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