Structure of Atom Chapter-Wise Test 14

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The electronic configuration of an element is \( 1s^2 2s^2 2p^6 3s^2 3p^3 \). What is the atomic number of this element?

Total electrons = 2 + 2 + 6 + 2 + 3 = 15. Atomic number = 15.

13
17
10
15
4

The ratio of the wavelengths of the first lines in the Lyman and Balmer series of a hydrogen atom is: (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Lyman (2→1): \( \bar{v} = 1.097 \times 10^7 (1 - 1/4) = 8.2275 \times 10^6 \, \text{m}^{-1} \), \( \lambda_1 = 1.215 \times 10^{-7} \, \text{m} \). Balmer (3→2): \( \bar{v} = 1.097 \times 10^7 (1/4 - 1/9) = 1.5236 \times 10^6 \, \text{m}^{-1} \), \( \lambda_2 = 6.563 \times 10^{-7} \, \text{m} \). Ratio = \( \lambda_1 / \lambda_2 = 1.215 \times 10^{-7} / 6.563 \times 10^{-7} \approx 0.185 \).

\( 5.4 \)
\( 0.185 \)
\( 2.7 \)
\( 1.0 \)
2

The de Broglie wavelength of a proton moving at \( 1.0 \times 10^6 \, \text{m s}^{-1} \) is: (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_p = 1.67 \times 10^{-27} \, \text{kg} \))

\( \lambda = \frac{h}{m v} = \frac{6.626 \times 10^{-34}}{1.67 \times 10^{-27} \times 1.0 \times 10^6} = 3.966 \times 10^{-13} \, \text{m} \).

\( 3.966 \times 10^{-13} \, \text{m} \)
\( 6.626 \times 10^{-13} \, \text{m} \)
\( 1.983 \times 10^{-13} \, \text{m} \)
\( 3.313 \times 10^{-13} \, \text{m} \)
1

An ion has 17 protons and 18 electrons. What is its charge?

Charge = protons - electrons = 17 - 18 = -1.

\( +1 \)
\( -1 \)
\( +2 \)
\( 0 \)
2

How many possible sets of quantum numbers (\( n, l, m_l, m_s \)) are there for electrons in the \( n = 4 \) energy level?

For \( n = 4 \), orbitals = \( 4^2 = 16 \) (4s: 1, 4p: 3, 4d: 5, 4f: 7). Each orbital has 2 electrons, total sets = \( 16 \times 2 = 32 \).

16
18
32
24
3

An element has 20 protons and 20 neutrons. What is its atomic mass number?

Mass number \( A = \) protons + neutrons = 20 + 20 = 40.

20
30
50
40
4

The ratio of the kinetic energies of an electron in the second orbit of \( \text{He}^+ \) to the third orbit of \( \text{H} \) is: (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

For \( \text{He}^+ \) (Z = 2), \( v_2 = 2 \times 2.19 \times 10^6 / 2 = 2.19 \times 10^6 \, \text{m s}^{-1} \), \( KE_2 = 2.18 \times 10^{-18} \, \text{J} \). For \( \text{H} \) (Z = 1), \( v_3 = 2.19 \times 10^6 / 3 = 7.3 \times 10^5 \, \text{m s}^{-1} \), \( KE_3 = 2.42 \times 10^{-19} \, \text{J} \). Ratio = \( 2.18 \times 10^{-18} / 2.42 \times 10^{-19} \approx 9 \).

\( 4 \)
\( 6 \)
\( 12 \)
\( 9 \)
4

The ratio of the radii of the fourth orbit of \( \text{H} \) to the third orbit of \( \text{Be}^{3+} \) is: (\( r_1 \) for H = \( 5.29 \times 10^{-11} \, \text{m} \))

For \( \text{H} \) (Z = 1), \( r_4 = 16 \times 5.29 \times 10^{-11} = 8.464 \times 10^{-10} \, \text{m} \). For \( \text{Be}^{3+} \) (Z = 4), \( r_3 = 9 \times 5.29 \times 10^{-11} / 4 = 1.19025 \times 10^{-10} \, \text{m} \). Ratio = \( 8.464 \times 10^{-10} / 1.19025 \times 10^{-10} \approx 7.11 \).

\( 4.0 \)
\( 7.11 \)
\( 2.25 \)
\( 9.0 \)
2

The energy required to excite an electron from \( n = 2 \) to \( n = 5 \) in a hydrogen atom is \( 4.896 \times 10^{-19} \, \text{J} \). What is the wavelength of the absorbed photon? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

\( \lambda = \frac{hc}{\Delta E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{4.896 \times 10^{-19}} = 4.061 \times 10^{-7} \, \text{m} = 406.1 \, \text{nm} \).

\( 486.1 \, \text{nm} \)
\( 656.3 \, \text{nm} \)
\( 406.1 \, \text{nm} \)
\( 364.6 \, \text{nm} \)
3

An electron and an alpha particle have the same de Broglie wavelength. What is the ratio of their velocities? (\( m_e = 9.1 \times 10^{-31} \, \text{kg} \), \( m_{\alpha} = 6.64 \times 10^{-27} \, \text{kg} \))

\( \lambda = \frac{h}{mv} \). For equal \( \lambda \), \( m_e v_e = m_{\alpha} v_{\alpha} \). \( v_e / v_{\alpha} = m_{\alpha} / m_e = 6.64 \times 10^{-27} / 9.1 \times 10^{-31} \approx 7297 \).

\( 4 \)
\( 7297 \)
\( 1836 \)
\( 0.000137 \)
2

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