Atoms and Nuclei Chapter-Wise Test 5

Correct answer Carries: 4.

Wrong Answer Carries: -1.

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

\( E_5 = -\frac{13.6}{5^2} = -\frac{13.6}{25} = -0.544 \, \text{eV} \).

-1.51 eV
-0.544 eV
-3.4 eV
-0.85 eV
2

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

\( r_n = n^2 r_1 \), \( r_4 = 4^2 \times 5.3 \times 10^{-11} = 8.48 \times 10^{-10} \, \text{m} \).

Circumference = \( 2\pi r_4 = 2 \times 3.14 \times 8.48 \times 10^{-10} \approx 5.33 \times 10^{-9} \, \text{m} \).

\( 5.33 \times 10^{-9} \, \text{m} \)
\( 3.0 \times 10^{-9} \, \text{m} \)
\( 1.33 \times 10^{-9} \, \text{m} \)
\( 2.12 \times 10^{-9} \, \text{m} \)
1

In the Bohr model, what is the ground state of a hydrogen atom?

The ground state is the lowest energy state, where the electron is in the orbit with \( n = 1 \), having an energy of -13.6 eV.

State with \( n = 2 \)
State with zero energy
State with \( n = 1 \)
State with infinite radius
3

In Rutherford’s scattering experiment, what fraction of alpha-particles scatter by more than 90° out of 8000 incident particles?

Given: 1 in 8000 alpha-particles deflect by more than 90°.

Fraction = \( \frac{1}{8000} = 0.000125 \).

0.000125
0.0014
0.01
0.00025
1

Which of the following is a key feature of Bohr’s model for the hydrogen atom?

Bohr’s model introduces quantization, where electrons revolve in stable orbits with angular momentum as integral multiples of \( h/2\pi \).

Electrons have quantized angular momentum
Electrons emit radiation continuously
Positive charge is distributed uniformly
Nucleus orbits the electrons
1

In Rutherford’s model, what is the order of magnitude of the ratio of the atomic size to the nuclear size?

Atomic size \( \approx 10^{-10} \, \text{m} \), nuclear size \( \approx 10^{-15} \, \text{m} \).

Ratio = \( \frac{10^{-10}}{10^{-15}} = 10^5 \).

\( 10^3 \)
\( 10^4 \)
\( 10^5 \)
\( 10^6 \)
3

In Rutherford’s model, what provides the centripetal force for an electron orbiting the nucleus in a hydrogen atom?

The electrostatic force between the electron and nucleus provides the centripetal force: \( \frac{e^2}{4\pi\epsilon_0 r^2} = \frac{m v^2}{r} \).

Gravitational force
Magnetic force
Electrostatic force
Nuclear force
3

An electron in a hydrogen atom has a speed of \( 2.2 \times 10^6 \, \text{m/s} \) in the first orbit. What is its kinetic energy? (Mass of electron = \( 9.1 \times 10^{-31} \, \text{kg} \), 1 eV = \( 1.6 \times 10^{-19} \, \text{J} \))

\( K = \frac{1}{2} m v^2 = \frac{1}{2} \times 9.1 \times 10^{-31} \times (2.2 \times 10^6)^2 \).

\( K = 2.2 \times 10^{-18} \, \text{J} = \frac{2.2 \times 10^{-18}}{1.6 \times 10^{-19}} \approx 13.75 \, \text{eV} \approx 13.6 \, \text{eV} \).

13.6 eV
6.8 eV
27.2 eV
3.4 eV
1

What is the wavelength of the photon emitted when an electron in a hydrogen atom drops from \( n = 3 \) to \( n = 2 \)? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \), \( c = 3 \times 10^8 \, \text{m/s} \), 1 eV = \( 1.6 \times 10^{-19} \, \text{J} \))

\( E_3 = -1.51 \, \text{eV} \), \( E_2 = -3.4 \, \text{eV} \).

\( \Delta E = 1.89 \, \text{eV} = 1.89 \times 1.6 \times 10^{-19} = 3.024 \times 10^{-19} \, \text{J} \).

\( \lambda = \frac{hc}{\Delta E} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{3.024 \times 10^{-19}} \approx 6.56 \times 10^{-7} \, \text{m} \).

\( 4.86 \times 10^{-7} \, \text{m} \)
\( 5.12 \times 10^{-7} \, \text{m} \)
\( 6.12 \times 10^{-7} \, \text{m} \)
\( 6.56 \times 10^{-7} \, \text{m} \)
4

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

Thomson’s model describes the atom as a sphere of positive charge with electrons embedded in it, resembling a plum pudding, not a nuclear structure.

Positive charge is spread uniformly with electrons embedded in it
Positive charge is concentrated in a small nucleus
Electrons orbit the nucleus like planets
Atom consists of discrete energy levels
1

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