Structure of Atom Chapter-Wise Test 12

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A metal has a threshold frequency of \( 4.8 \times 10^{14} \, \text{Hz} \). What is the kinetic energy of an electron ejected by light of frequency \( 7.2 \times 10^{14} \, \text{Hz} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( W_0 = h v_0 = 6.626 \times 10^{-34} \times 4.8 \times 10^{14} = 3.1805 \times 10^{-19} \, \text{J} \). \( E = h v = 6.626 \times 10^{-34} \times 7.2 \times 10^{14} = 4.7707 \times 10^{-19} \, \text{J} \). \( KE = 4.7707 \times 10^{-19} - 3.1805 \times 10^{-19} = 1.5902 \times 10^{-19} \, \text{J} \).

\( 3.1805 \times 10^{-19} \, \text{J} \)
\( 1.5902 \times 10^{-19} \, \text{J} \)
\( 4.7707 \times 10^{-19} \, \text{J} \)
\( 2.3854 \times 10^{-19} \, \text{J} \)
2

The energy of an electron in the second orbit of \( \text{Be}^{3+} \) is \( -19.36 \, \text{eV} \). What is the ionization energy from the fifth orbit? (\( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

For \( \text{Be}^{3+} \) (Z = 4), \( E_n = -77.44 / n^2 \). \( E_5 = -77.44 / 25 = -3.0976 \, \text{eV} \). Ionization energy = \( 0 - (-3.0976) = 3.0976 \, \text{eV} \).

\( 19.36 \, \text{eV} \)
\( 3.0976 \, \text{eV} \)
\( 12.39 \, \text{eV} \)
\( 6.195 \, \text{eV} \)
2

The ionization energy of a hydrogen atom is \( 13.6 \, \text{eV} \). What is the wavelength of the photon emitted when an electron in \( \text{B}^{4+} \) falls from \( n = 5 \) to \( n = 2 \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

For \( \text{B}^{4+} \) (Z = 5), \( E_n = -13.6 \times Z^2 / n^2 \). \( E_2 = -13.6 \times 25 / 4 = -85 \, \text{eV} \), \( E_5 = -13.6 \times 25 / 25 = -13.6 \, \text{eV} \). \( \Delta E = -13.6 - (-85) = 71.4 \, \text{eV} = 1.1424 \times 10^{-17} \, \text{J} \). \( \lambda = \frac{hc}{\Delta E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{1.1424 \times 10^{-17}} = 1.741 \times 10^{-8} \, \text{m} = 17.41 \, \text{nm} \).

\( 17.41 \, \text{nm} \)
\( 34.82 \, \text{nm} \)
\( 12.16 \, \text{nm} \)
\( 24.32 \, \text{nm} \)
1

An electron in a hydrogen atom transitions from \( n = 3 \) to \( n = 2 \). What is the wavenumber of the emitted light? (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Wavenumber \( \bar{v} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = 1.097 \times 10^7 \left( \frac{1}{4} - \frac{1}{9} \right) = 1.5236 \times 10^6 \, \text{m}^{-1} \).

\(2.742 \times 10^6 \, \text{m}^{-1}\)
\(1.5236 \times 10^6 \, \text{m}^{-1}\)
\(3.291 \times 10^6 \, \text{m}^{-1}\)
\(1.097 \times 10^7 \, \text{m}^{-1}\)
2

Which of the following transitions in a hydrogen atom emits light of the longest wavelength?

Longest wavelength (lowest energy) occurs for the smallest \( \Delta E \). \( n = 4 \) to \( n = 3 \) has the smallest energy difference among the options.

\( n = 2 \) to \( n = 1 \)
\( n = 4 \) to \( n = 3 \)
\( n = 3 \) to \( n = 2 \)
\( n = 5 \) to \( n = 4 \)
2

A photon has an energy of \( 4.968 \times 10^{-19} \, \text{J} \). What is its wavelength in nanometers? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

\( E = \frac{hc}{\lambda} \), so \( \lambda = \frac{hc}{E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{4.968 \times 10^{-19}} = 4.0 \times 10^{-7} \, \text{m} = 400 \, \text{nm} \).

\( 400 \, \text{nm} \)
\( 500 \, \text{nm} \)
\( 300 \, \text{nm} \)
\( 600 \, \text{nm} \)
1

How many spectral lines are observed when an electron falls from \( n = 4 \) to \( n = 2 \) in a hydrogen atom?

Transitions: 4→2, 4→3→2, 3→2. Total lines = 3.

1
2
4
3
4

The uncertainty in the position of an electron is \( 1.0 \times 10^{-10} \, \text{m} \). What is the minimum uncertainty in its velocity? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Heisenberg’s principle: \( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \). \( \Delta p = m_e \Delta v \), so \( \Delta v \geq \frac{h}{4\pi m_e \Delta x} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 1.0 \times 10^{-10}} = 5.8 \times 10^5 \, \text{m s}^{-1} \).

\( 2.9 \times 10^5 \, \text{m s}^{-1} \)
\( 1.45 \times 10^5 \, \text{m s}^{-1} \)
\( 5.8 \times 10^5 \, \text{m s}^{-1} \)
\( 7.3 \times 10^5 \, \text{m s}^{-1} \)
3

An electron in \( \text{Li}^{2+} \) is in the \( n = 2 \) state. What is its energy in joules? (\( E_1 \) for H = \( -2.18 \times 10^{-18} \, \text{J} \))

For \( \text{Li}^{2+} \) (Z = 3), \( E_n = -Z^2 \times E_1 / n^2 \). \( E_2 = -3^2 \times 2.18 \times 10^{-18} / 2^2 = -9 \times 2.18 \times 10^{-18} / 4 = -4.905 \times 10^{-18} \, \text{J} \).

\( -4.905 \times 10^{-18} \, \text{J} \)
\( -2.18 \times 10^{-18} \, \text{J} \)
\( -1.962 \times 10^{-17} \, \text{J} \)
\( -5.45 \times 10^{-19} \, \text{J} \)
1

The angular momentum of an electron in the fifth Bohr orbit is: (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( L = \frac{nh}{2\pi} \). For \( n = 5 \), \( L = \frac{5 \times 6.626 \times 10^{-34}}{2 \times 3.14} = 5.275 \times 10^{-34} \, \text{J s} \).

\( 2.11 \times 10^{-34} \, \text{J s} \)
\( 3.313 \times 10^{-34} \, \text{J s} \)
\( 1.055 \times 10^{-34} \, \text{J s} \)
\( 5.275 \times 10^{-34} \, \text{J s} \)
4

Performance Summary

Score:

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