Atoms and Nuclei Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

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

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

For \( n = 2 \): \( r_2 = 2^2 \times 5.3 \times 10^{-11} = 4 \times 5.3 \times 10^{-11} = 2.12 \times 10^{-10} \, \text{m} \).

\( 2.12 \times 10^{-10} \, \text{m} \)
\( 1.06 \times 10^{-10} \, \text{m} \)
\( 4.24 \times 10^{-10} \, \text{m} \)
\( 5.3 \times 10^{-11} \, \text{m} \)
1

Which of the following statements is correct about the energy levels in a hydrogen atom according to Bohr’s model?

The energy becomes less negative (increases) as the principal quantum number \( n \) increases, approaching zero at \( n = \infty \).

Energy decreases with increasing \( n \)
Energy increases with increasing \( n \)
Energy is constant for all orbits
Energy is zero in the ground state
2

A hydrogen atom in the \( n = 5 \) state emits a photon and returns to the ground state. What is the maximum energy of the photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_5 = -0.544 \, \text{eV} \), \( E_1 = -13.6 \, \text{eV} \).

\( \Delta E = -0.544 - (-13.6) = 13.056 \, \text{eV} \approx 13.06 \, \text{eV} \).

12.09 eV
2.86 eV
10.2 eV
13.06 eV
4

How many de Broglie wavelengths fit into the circumference of the \( n = 4 \) orbit of a hydrogen atom?

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

For \( n = 4 \), number of wavelengths = 4.

2
3
5
4
4

What is the ratio of the kinetic energy to the potential energy of an electron in the ground state of a hydrogen atom? (Given total energy = -13.6 eV)

\( E = K + U \), \( K = 13.6 \, \text{eV} \), \( U = -27.2 \, \text{eV} \).

Ratio = \( \frac{K}{|U|} = \frac{13.6}{27.2} = 0.5 \).

0.5
1
2
-0.5
1

What is the wavelength of a photon emitted when an electron drops from \( n = 4 \) to \( n = 3 \) in a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \), \( c = 3 \times 10^8 \, \text{m/s} \), 1 eV = \( 1.6 \times 10^{-19} \, \text{J} \))

\( \Delta E = 0.66 \, \text{eV} = 1.056 \times 10^{-19} \, \text{J} \).

\( \lambda = \frac{hc}{\Delta E} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{1.056 \times 10^{-19}} \approx 1.875 \times 10^{-6} \, \text{m} \).

\( 4.33 \times 10^{-7} \, \text{m} \)
\( 6.56 \times 10^{-7} \, \text{m} \)
\( 1.21 \times 10^{-7} \, \text{m} \)
\( 1.875 \times 10^{-6} \, \text{m} \)
4

What is the angular momentum of an electron in the \( n = 5 \) state of a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \))

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

For \( n = 5 \): \( L = 5 \times \frac{6.6 \times 10^{-34}}{2 \times 3.14} \approx 5.25 \times 10^{-34} \, \text{J·s} \).

\( 2.1 \times 10^{-34} \, \text{J·s} \)
\( 5.25 \times 10^{-34} \, \text{J·s} \)
\( 3.15 \times 10^{-34} \, \text{J·s} \)
\( 1.05 \times 10^{-34} \, \text{J·s} \)
2

A hydrogen atom absorbs a photon and jumps from \( n = 1 \) to \( n = 2 \). What is the energy of the photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_1 = -13.6 \, \text{eV} \), \( E_2 = -\frac{13.6}{2^2} = -3.4 \, \text{eV} \).

\( \Delta E = E_2 - E_1 = -3.4 - (-13.6) = 10.2 \, \text{eV} \).

13.6 eV
10.2 eV
3.4 eV
1.51 eV
2

In Rutherford’s model, what is the primary force keeping electrons in orbit around the nucleus?

The electrostatic force of attraction between the positively charged nucleus and negatively charged electrons provides the centripetal force for orbiting.

Gravitational force
Magnetic force
Nuclear force
Electrostatic force
4

The radius of the third orbit in a hydrogen atom is how many times the radius of the first orbit if \( r_1 = 5.3 \times 10^{-11} \, \text{m} \)?

\( r_n = n^2 r_1 \).

For \( n = 3 \): \( r_3 = 3^2 \times 5.3 \times 10^{-11} = 9 \times 5.3 \times 10^{-11} = 4.77 \times 10^{-10} \, \text{m} \).

Ratio = \( \frac{r_3}{r_1} = 9 \).

4
6
9
12
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