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  4. Structure of Atom Chapter-Wise Test 4

Structure of Atom Chapter-Wise Test 4

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A photon of wavelength \( 200 \, \text{nm} \) ejects an electron from a metal with a velocity of \( 6.62 \times 10^5 \, \text{m s}^{-1} \). What is the work function of the metal? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Photon energy \( E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{200 \times 10^{-9}} = 9.939 \times 10^{-19} \, \text{J} \). \( KE = \frac{1}{2} m v^2 = \frac{1}{2} \times 9.1 \times 10^{-31} \times (6.62 \times 10^5)^2 = 1.994 \times 10^{-19} \, \text{J} \). \( W_0 = E - KE = 9.939 \times 10^{-19} - 1.994 \times 10^{-19} = 7.945 \times 10^{-19} \, \text{J} \).

\( 7.945 \times 10^{-19} \, \text{J} \)
\( 9.939 \times 10^{-19} \, \text{J} \)
\( 1.994 \times 10^{-19} \, \text{J} \)
\( 5.963 \times 10^{-19} \, \text{J} \)
1

The number of spectral lines produced when an electron in a hydrogen atom falls from \( n = 5 \) to \( n = 2 \) is:

Transitions: 5→2, 5→3→2, 5→4→2, 4→2, 3→2. Total = 5 lines.

3
5
6
4
2

What is the maximum number of electrons that can occupy the subshell with principal quantum number \( n = 2 \) and azimuthal quantum number \( l = 1 \)?

For \( l = 1 \) (p subshell), number of orbitals = \( 2l + 1 = 3 \). Each orbital holds 2 electrons, so total = \( 3 \times 2 = 6 \).

2
6
10
4
2

The number of electrons in an atom with quantum numbers \( n = 4, l = 1, m_l = 0 \) is:

For \( n = 4, l = 1, m_l = 0 \) (one specific 4p orbital), electrons = 2 (spin \( m_s = +1/2 \) and \( -1/2 \)).

6
2
4
1
2

What is the wavelength of the second line in the Balmer series of a hydrogen atom? (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Second line: \( n = 4 \) to \( n = 2 \). \( \bar{v} = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{4^2} \right) = 2.057 \times 10^6 \, \text{m}^{-1} \). \( \lambda = \frac{1}{\bar{v}} = 4.861 \times 10^{-7} \, \text{m} = 486.1 \, \text{nm} \).

\( 656.3 \, \text{nm} \)
\( 410.2 \, \text{nm} \)
\( 121.6 \, \text{nm} \)
\( 486.1 \, \text{nm} \)
4

A metal has a threshold wavelength of \( 450 \, \text{nm} \). What is the kinetic energy of an electron ejected by light of wavelength \( 300 \, \text{nm} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

\( W_0 = \frac{hc}{\lambda_0} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{450 \times 10^{-9}} = 4.417 \times 10^{-19} \, \text{J} \). Photon energy \( E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{300 \times 10^{-9}} = 6.626 \times 10^{-19} \, \text{J} \). \( KE = E - W_0 = 6.626 \times 10^{-19} - 4.417 \times 10^{-19} = 2.209 \times 10^{-19} \, \text{J} \).

\( 4.417 \times 10^{-19} \, \text{J} \)
\( 2.209 \times 10^{-19} \, \text{J} \)
\( 6.626 \times 10^{-19} \, \text{J} \)
\( 1.475 \times 10^{-19} \, \text{J} \)
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 \( \text{Li}^{2+} \) 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 \( \text{Li}^{2+} \) (Z = 3), \( E_n = -13.6 \times Z^2 / n^2 \). \( E_2 = -13.6 \times 9 / 4 = -30.6 \, \text{eV} \), \( E_5 = -13.6 \times 9 / 25 = -4.896 \, \text{eV} \). \( \Delta E = -4.896 - (-30.6) = 25.704 \, \text{eV} = 4.1126 \times 10^{-18} \, \text{J} \). \( \lambda = \frac{hc}{\Delta E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{4.1126 \times 10^{-18}} = 4.834 \times 10^{-8} \, \text{m} = 48.34 \, \text{nm} \).

\( 48.34 \, \text{nm} \)
\( 121.6 \, \text{nm} \)
\( 30.6 \, \text{nm} \)
\( 97.2 \, \text{nm} \)
1

An electron in the second orbit of \( \text{He}^+ \) has a velocity of \( 2.19 \times 10^6 \, \text{m s}^{-1} \). What is its de Broglie wavelength? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( \lambda = \frac{h}{m v} = \frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 2.19 \times 10^6} = 3.325 \times 10^{-10} \, \text{m} \).

\( 3.325 \times 10^{-10} \, \text{m} \)
\( 6.65 \times 10^{-10} \, \text{m} \)
\( 1.663 \times 10^{-10} \, \text{m} \)
\( 9.975 \times 10^{-10} \, \text{m} \)
1

The velocity of an electron in the second orbit of a hydrogen atom is \( 1.095 \times 10^6 \, \text{m s}^{-1} \). What is its de Broglie wavelength in this orbit? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( \lambda = \frac{h}{m v} = \frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 1.095 \times 10^6} = 6.65 \times 10^{-10} \, \text{m} \). (Note: Matches Bohr’s \( \lambda = 2\pi r_n \) for \( n = 2 \), confirming consistency).

\( 6.65 \times 10^{-10} \, \text{m} \)
\( 3.33 \times 10^{-10} \, \text{m} \)
\( 9.98 \times 10^{-10} \, \text{m} \)
\( 1.66 \times 10^{-10} \, \text{m} \)
1

The threshold frequency for a metal is \( 6.0 \times 10^{14} \, \text{Hz} \). What is the work function in joules? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Work function \( W_0 = h v_0 = 6.626 \times 10^{-34} \times 6.0 \times 10^{14} = 3.9756 \times 10^{-19} \, \text{J} \).

\(2.6504 \times 10^{-19} \, \text{J}\)
\(3.9756 \times 10^{-19} \, \text{J}\)
\(5.3008 \times 10^{-19} \, \text{J}\)
\(1.9878 \times 10^{-19} \, \text{J}\)
2

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