Atoms and Nuclei Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What characterizes the emission line spectrum of a hydrogen atom?

The emission line spectrum consists of bright lines on a dark background, corresponding to specific wavelengths emitted during electron transitions.

Continuous band of colors
Dark lines on a bright background
Random light flashes
Bright lines on a dark background
4

In Bohr’s model, what defines the stationary orbits of an electron?

Bohr’s second postulate defines stationary orbits as those where the angular momentum is an integral multiple of \( h/2\pi \).

Continuous energy levels
Quantized angular momentum
Random electron paths
Uniform charge distribution
2

In Bohr’s model, what is the state of a hydrogen atom when its electron is in the \( n = \infty \) orbit?

At \( n = \infty \), the energy is zero, meaning the electron is ionized and no longer bound to the nucleus.

Ground state
First excited state
Ionized state
Unstable state
3

What does the de Broglie hypothesis suggest about the electron in Bohr’s model?

De Broglie suggests that electrons exhibit wave-like behavior, forming standing waves in orbits where the circumference is an integer multiple of the wavelength.

Electrons are stationary
Electrons emit continuous radiation
Electrons have no wave properties
Electrons form standing waves
4

In the Bohr model, how many de Broglie wavelengths fit into the circumference of the \( n = 6 \) orbit?

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

For \( n = 6 \), number of wavelengths = 6.

4
5
3
6
4

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

Rutherford’s model does not explain atomic stability, as it predicts electrons would emit radiation and collapse into the nucleus, not maintain stable orbits.

Electrons maintain stable orbits without radiating
Positive charge is concentrated in the nucleus
Most of the atom is empty space
Nucleus is small and dense
1

An electron in a hydrogen atom transitions from \( n = 3 \) to \( n = 1 \). What is the energy of the emitted photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_3 = -\frac{13.6}{3^2} = -1.51 \, \text{eV} \), \( E_1 = -13.6 \, \text{eV} \).

\( \Delta E = E_3 - E_1 = -1.51 - (-13.6) = 12.09 \, \text{eV} \).

10.2 eV
12.09 eV
13.6 eV
1.89 eV
2

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

\( E_4 = -\frac{13.6}{4^2} = -\frac{13.6}{16} = -0.85 \, \text{eV} \).

-1.51 eV
-0.85 eV
-3.4 eV
-13.6 eV
2

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

\( \Delta E = 10.2 \, \text{eV} = 1.632 \times 10^{-18} \, \text{J} \).

\( \lambda = \frac{hc}{\Delta E} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{1.632 \times 10^{-18}} \approx 1.21 \times 10^{-7} \, \text{m} \).

\( 6.56 \times 10^{-7} \, \text{m} \)
\( 4.86 \times 10^{-7} \, \text{m} \)
\( 1.89 \times 10^{-7} \, \text{m} \)
\( 1.21 \times 10^{-7} \, \text{m} \)
4

What is the energy difference between the \( n = 5 \) and \( n = 3 \) states in a hydrogen atom? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_5 = -0.544 \, \text{eV} \), \( E_3 = -1.51 \, \text{eV} \).

\( \Delta E = -0.544 - (-1.51) = 0.966 \, \text{eV} \approx 0.97 \, \text{eV} \).

1.89 eV
0.66 eV
0.97 eV
2.86 eV
3

Performance Summary

Score:

Category Details
Total Attempts:
Total Skipped:
Total Wrong Answers:
Total Correct Answers:
Time Taken:
Average Time Taken per Question:
Accuracy:
0