Structure of Atom Chapter-Wise Test 13

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the velocity of an electron in the third orbit of \( \text{He}^+ \)? (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \))

For hydrogen-like atoms, \( v_n = \frac{Z v_1}{n} \). For \( \text{He}^+ \) (Z = 2), \( n = 3 \), \( v_3 = \frac{2 \times 2.19 \times 10^6}{3} = 1.46 \times 10^6 \, \text{m s}^{-1} \).

\( 7.3 \times 10^5 \, \text{m s}^{-1} \)
\( 2.19 \times 10^6 \, \text{m s}^{-1} \)
\( 1.46 \times 10^6 \, \text{m s}^{-1} \)
\( 4.38 \times 10^6 \, \text{m s}^{-1} \)
3

Which of the following species has the same number of electrons as \( \text{Na}^+ \) (atomic number 11)?

\( \text{Na}^+ \) has 10 electrons (11 - 1). \( \text{Mg}^{2+} \) (12 - 2 = 10) also has 10 electrons.

\( \text{K}^+ \)
\( \text{Mg}^{2+} \)
\( \text{Ca}^{2+} \)
\( \text{S}^{2-} \)
2

Which orbital is represented by the quantum numbers \( n = 3, l = 1 \)?

\( n = 3, l = 1 \) corresponds to the 3p orbital.

3s
3d
3p
4p
3

How many orbitals in an atom can have the quantum numbers \( n = 5 \) and \( l = 3 \)?

For \( l = 3 \) (f subshell), orbitals = \( 2l + 1 = 2 \times 3 + 1 = 7 \).

9
7
5
11
2

The ionization energy of a hydrogen atom from its ground state is \( 2.18 \times 10^{-18} \, \text{J} \). What is the energy required to ionize \( \text{He}^+ \) from its ground state?

For \( \text{He}^+ \) (Z = 2), \( E = Z^2 \times E_H = 4 \times 2.18 \times 10^{-18} = 8.72 \times 10^{-18} \, \text{J} \).

\(4.36 \times 10^{-18} \, \text{J}\)
\(2.18 \times 10^{-18} \, \text{J}\)
\(8.72 \times 10^{-18} \, \text{J}\)
\(1.09 \times 10^{-18} \, \text{J}\)
3

Which of the following represents the electronic configuration of an element with atomic number 16?

Atomic number 16: \( 1s^2 2s^2 2p^6 3s^2 3p^4 \) (sulfur).

\( 1s^2 2s^2 2p^6 3s^2 3p^2 \)
\( 1s^2 2s^2 2p^6 3s^2 3p^6 \)
\( 1s^2 2s^2 2p^6 3s^1 3p^5 \)
\( 1s^2 2s^2 2p^6 3s^2 3p^4 \)
4

The kinetic energy of an electron in the first orbit of \( \text{He}^+ \) is \( 4.36 \times 10^{-18} \, \text{J} \). What is its velocity? (\( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( KE = \frac{1}{2} m v^2 \), \( v = \sqrt{\frac{2 \times 4.36 \times 10^{-18}}{9.1 \times 10^{-31}}} = \sqrt{9.582 \times 10^{12}} = 3.096 \times 10^6 \, \text{m s}^{-1} \).

\( 2.19 \times 10^6 \, \text{m s}^{-1} \)
\( 4.38 \times 10^6 \, \text{m s}^{-1} \)
\( 3.096 \times 10^6 \, \text{m s}^{-1} \)
\( 1.548 \times 10^6 \, \text{m s}^{-1} \)
3

A photon of frequency \( 6.0 \times 10^{14} \, \text{Hz} \) strikes a metal surface with a work function of \( 2.5 \times 10^{-19} \, \text{J} \). What is the kinetic energy of the ejected electron? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Photon energy \( E = h v = 6.626 \times 10^{-34} \times 6.0 \times 10^{14} = 3.9756 \times 10^{-19} \, \text{J} \). \( KE = E - W_0 = 3.9756 \times 10^{-19} - 2.5 \times 10^{-19} = 1.4756 \times 10^{-19} \, \text{J} \).

\( 1.4756 \times 10^{-19} \, \text{J} \)
\( 2.5 \times 10^{-19} \, \text{J} \)
\( 3.9756 \times 10^{-19} \, \text{J} \)
\( 6.626 \times 10^{-19} \, \text{J} \)
1

The number of spectral lines in the Brackett series when an electron falls from \( n = 7 \) to \( n = 4 \) in a hydrogen atom is:

Transitions: 7→4, 7→5→4, 7→6→4, 6→4, 5→4. Total = 5 lines.

3
6
4
5
4

How many possible values of \( m_l \) are there for an electron with \( n = 3, l = 2 \)?

For \( l = 2 \), \( m_l = -2, -1, 0, +1, +2 \). Total = 5 values.

3
5
7
1
2

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