Atoms and Nuclei Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

An electron beam of 11.0 eV excites a hydrogen atom in the ground state. What is the highest energy level reached? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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

\( E_n = -13.6 + 11.0 = -2.6 \, \text{eV} \).

\( -2.6 = -\frac{13.6}{n^2} \Rightarrow n^2 \approx 5.23 \Rightarrow n = 2 \) (since \( E_2 = -3.4 \, \text{eV} < -2.6 \, \text{eV} \)).

1
3
4
2
4

In Rutherford’s scattering experiment, what happens to an alpha-particle with a large impact parameter?

For a large impact parameter, the alpha-particle experiences minimal deflection (\( \theta \approx 0 \)) and goes nearly undeviated.

Rebounds back
Scatters at 90°
Goes nearly undeviated
Stops completely
3

What is the energy required to excite a hydrogen atom from \( n = 1 \) to \( n = 3 \)? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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

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

10.2 eV
1.89 eV
12.09 eV
2.55 eV
3

Which of the following statements is correct about the Bohr model’s prediction of hydrogen spectra?

The model predicts discrete frequencies because photon energy equals the difference between quantized energy levels, not continuous radiation.

Emits continuous frequencies
Based on nuclear size
Predicts discrete frequencies
Depends on electron mass only
3

A hydrogen atom is excited to the \( n = 4 \) state and returns to the ground state. What is the maximum energy of the emitted photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

\( E_4 = -0.85 \, \text{eV} \), \( E_1 = -13.6 \, \text{eV} \).

\( \Delta E = -0.85 - (-13.6) = 12.75 \, \text{eV} \).

10.2 eV
2.55 eV
1.89 eV
12.75 eV
4

An electron in a hydrogen atom has an angular momentum of \( 1.05 \times 10^{-34} \, \text{J·s} \). What is its principal quantum number? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \))

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

\( 1.05 \times 10^{-34} = n \times \frac{6.6 \times 10^{-34}}{2 \times 3.14} \).

\( n = 1 \).

2
1
3
4
2

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

\( r_n = n^2 r_1 \), \( r_3 = 3^2 \times 5.3 \times 10^{-11} = 4.77 \times 10^{-10} \, \text{m} \).

Circumference = \( 2\pi r_3 = 2 \times 3.14 \times 4.77 \times 10^{-10} \approx 3.0 \times 10^{-9} \, \text{m} \).

\( 3.0 \times 10^{-9} \, \text{m} \)
\( 2.0 \times 10^{-9} \, \text{m} \)
\( 1.5 \times 10^{-9} \, \text{m} \)
\( 4.0 \times 10^{-9} \, \text{m} \)
1

What is the ratio of the radius of the \( n = 4 \) orbit to the \( n = 2 \) orbit in a hydrogen atom?

\( r_n = n^2 r_1 \).

\( r_4 = 16 r_1 \), \( r_2 = 4 r_1 \).

Ratio = \( \frac{r_4}{r_2} = \frac{16}{4} = 4 \).

2
8
4
16
3

What is the significance of the negative total energy of an electron in a hydrogen atom according to Bohr’s model?

The negative total energy indicates that the electron is bound to the nucleus, requiring energy to be supplied to free it.

Electron is bound to the nucleus
Electron moves freely in space
Electron emits continuous radiation
Electron has zero kinetic energy
1

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

\( E_2 = -\frac{13.6}{2^2} = -\frac{13.6}{4} = -3.4 \, \text{eV} \).

-13.6 eV
-6.8 eV
-3.4 eV
-1.51 eV
3

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