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  4. Structure of Atom Chapter-Wise Test 10

Structure of Atom Chapter-Wise Test 10

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The ionization energy of \( \text{Li}^{2+} \) from its ground state is how many times that of a hydrogen atom? (\( E_H = 2.18 \times 10^{-18} \, \text{J} \))

For \( \text{Li}^{2+} \) (Z = 3), \( E = Z^2 E_H = 9 \times 2.18 \times 10^{-18} \). Ratio = \( 9 \).

4
6
3
9
4

Which of the following has the same number of neutrons as \( ^{40}_{18}\text{Ar} \)?

Neutrons in \( ^{40}_{18}\text{Ar} \) = 40 - 18 = 22. For \( ^{41}_{19}\text{K} \), neutrons = 41 - 19 = 22.

\( ^{39}_{19}\text{K} \)
\( ^{42}_{20}\text{Ca} \)
\( ^{41}_{19}\text{K} \)
\( ^{40}_{20}\text{Ca} \)
3

A metal has a work function of \( 2.5 \, \text{eV} \). What is the threshold wavelength? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

\( W_0 = 2.5 \times 1.6 \times 10^{-19} = 4.0 \times 10^{-19} \, \text{J} \). \( \lambda_0 = \frac{hc}{W_0} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{4.0 \times 10^{-19}} = 4.9695 \times 10^{-7} \, \text{m} = 496.95 \, \text{nm} \).

\( 620.5 \, \text{nm} \)
\( 354.2 \, \text{nm} \)
\( 443.7 \, \text{nm} \)
\( 496.95 \, \text{nm} \)
4

The uncertainty in position of a proton is \( 1.5 \times 10^{-11} \, \text{m} \). What is the minimum uncertainty in its momentum? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \), \( \Delta p \geq \frac{h}{4\pi \Delta x} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 1.5 \times 10^{-11}} = 3.52 \times 10^{-24} \, \text{kg m s}^{-1} \).

\( 1.76 \times 10^{-24} \, \text{kg m s}^{-1} \)
\( 5.27 \times 10^{-24} \, \text{kg m s}^{-1} \)
\( 3.52 \times 10^{-24} \, \text{kg m s}^{-1} \)
\( 2.64 \times 10^{-24} \, \text{kg m s}^{-1} \)
3

Which of the following sets of quantum numbers is not permissible for an electron?

For \( n = 3 \), \( l = 0 \) to 2. \( l = 3 \) exceeds the maximum value, making it invalid.

\( n = 3, l = 1, m_l = 0, m_s = +1/2 \)
\( n = 2, l = 0, m_l = 0, m_s = -1/2 \)
\( n = 3, l = 3, m_l = -2, m_s = +1/2 \)
\( n = 4, l = 2, m_l = +1, m_s = -1/2 \)
3

A metal has a work function of \( 2.8 \, \text{eV} \). What is the threshold wavelength? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

\( W_0 = 2.8 \times 1.6 \times 10^{-19} = 4.48 \times 10^{-19} \, \text{J} \). \( \lambda_0 = \frac{hc}{W_0} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{4.48 \times 10^{-19}} = 4.437 \times 10^{-7} \, \text{m} = 443.7 \, \text{nm} \).

\( 354.2 \, \text{nm} \)
\( 620.5 \, \text{nm} \)
\( 295.1 \, \text{nm} \)
\( 443.7 \, \text{nm} \)
4

An electron in the third orbit of a hydrogen atom has a velocity of \( 7.3 \times 10^5 \, \text{m s}^{-1} \). What is its de Broglie wavelength? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( \lambda = \frac{h}{m v} = \frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 7.3 \times 10^5} = 9.98 \times 10^{-10} \, \text{m} \).

\( 9.98 \times 10^{-10} \, \text{m} \)
\( 4.99 \times 10^{-10} \, \text{m} \)
\( 6.65 \times 10^{-10} \, \text{m} \)
\( 1.33 \times 10^{-9} \, \text{m} \)
1

Which of the following has the same number of electrons as \( \text{Ar} \) (atomic number 18)?

\( \text{Ar} \) has 18 electrons. \( \text{K}^+ \) (19 - 1 = 18) also has 18 electrons.

\( \text{Na}^+ \)
\( \text{Mg}^{2+} \)
\( \text{K}^+ \)
\( \text{Ca}^{2+} \)
3

The wavenumber of the fourth line in the Balmer series of a hydrogen atom is: (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Balmer series: \( n_1 = 2 \), fourth line is \( n_2 = 6 \). \( \bar{v} = R_H (1/2^2 - 1/6^2) = 1.097 \times 10^7 (1/4 - 1/36) = 1.097 \times 10^7 \times 8/36 = 2.437 \times 10^6 \, \text{m}^{-1} \).

\( 2.437 \times 10^6 \, \text{m}^{-1} \)
\( 1.523 \times 10^6 \, \text{m}^{-1} \)
\( 3.291 \times 10^6 \, \text{m}^{-1} \)
\( 2.057 \times 10^6 \, \text{m}^{-1} \)
1

The radius of the second orbit of a hydrogen atom is \( 2.116 \times 10^{-10} \, \text{m} \). What is the velocity of the electron in the fourth orbit? (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \))

For \( \text{H} \), \( r_n = n^2 r_1 \), \( r_1 = 5.29 \times 10^{-11} \, \text{m} \), \( r_2 = 4 \times 5.29 \times 10^{-11} = 2.116 \times 10^{-10} \, \text{m} \). \( v_n = \frac{v_1}{n} \), for \( n = 4 \), \( v_4 = \frac{2.19 \times 10^6}{4} = 5.475 \times 10^5 \, \text{m s}^{-1} \).

\( 1.095 \times 10^6 \, \text{m s}^{-1} \)
\( 5.475 \times 10^5 \, \text{m s}^{-1} \)
\( 7.3 \times 10^5 \, \text{m s}^{-1} \)
\( 2.19 \times 10^6 \, \text{m s}^{-1} \)
2

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