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  4. Structure of Atom Chapter-Wise Test 17

Structure of Atom Chapter-Wise Test 17

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A metal has a threshold frequency of \( 5.5 \times 10^{14} \, \text{Hz} \). What is the stopping potential when irradiated with light of frequency \( 8.0 \times 10^{14} \, \text{Hz} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

\( W_0 = h v_0 = 6.626 \times 10^{-34} \times 5.5 \times 10^{14} = 3.6443 \times 10^{-19} \, \text{J} \). \( E = h v = 6.626 \times 10^{-34} \times 8.0 \times 10^{14} = 5.3008 \times 10^{-19} \, \text{J} \). \( KE = 5.3008 \times 10^{-19} - 3.6443 \times 10^{-19} = 1.6565 \times 10^{-19} \, \text{J} \). \( V_s = KE / e = 1.035 \, \text{V} \).

A. \( 0.621 \, \text{V} \)
B. \( 1.656 \, \text{V} \)
C. \( 0.827 \, \text{V} \)
D. \( 1.035 \, \text{V} \)
4

The angular momentum of an electron in the sixth orbit of \( \text{Li}^{2+} \) is \( 6.33 \times 10^{-34} \, \text{J s} \). What is its radius? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( r_1 \) for H = \( 5.29 \times 10^{-11} \, \text{m} \))

\( n = \frac{L \cdot 2\pi}{h} = \frac{6.33 \times 10^{-34} \times 2 \times 3.14}{6.626 \times 10^{-34}} = 6 \). For \( \text{Li}^{2+} \) (Z = 3), \( r_6 = \frac{6^2}{3} \times 5.29 \times 10^{-11} = 12 \times 5.29 \times 10^{-11} = 6.348 \times 10^{-10} \, \text{m} \).

\( 6.348 \times 10^{-10} \, \text{m} \)
\( 3.174 \times 10^{-10} \, \text{m} \)
\( 1.058 \times 10^{-10} \, \text{m} \)
\( 9.522 \times 10^{-10} \, \text{m} \)
1

How many orbitals are present in the \( n = 3 \) energy level of an atom?

Number of orbitals = \( n^2 \). For \( n = 3 \), \( 3^2 = 9 \) (3s: 1, 3p: 3, 3d: 5).

9
4
16
25
1

The frequency of a photon emitted during a transition from \( n = 6 \) to \( n = 3 \) in a hydrogen atom is: (\( E_1 = -2.18 \times 10^{-18} \, \text{J} \), \( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( E_3 = -2.18 \times 10^{-18} / 9 = -2.422 \times 10^{-19} \, \text{J} \), \( E_6 = -2.18 \times 10^{-18} / 36 = -6.056 \times 10^{-20} \, \text{J} \). \( \Delta E = -6.056 \times 10^{-20} - (-2.422 \times 10^{-19}) = 1.8164 \times 10^{-19} \, \text{J} \). \( v = \frac{\Delta E}{h} = \frac{1.8164 \times 10^{-19}}{6.626 \times 10^{-34}} = 2.741 \times 10^{14} \, \text{Hz} \).

\( 2.741 \times 10^{14} \, \text{Hz} \)
\( 3.291 \times 10^{14} \, \text{Hz} \)
\( 1.645 \times 10^{14} \, \text{Hz} \)
\( 4.935 \times 10^{14} \, \text{Hz} \)
1

Which particle has the highest charge-to-mass ratio?

Electron has the highest \( e/m \) ratio (\( 1.758820 \times 10^{11} \, \text{C kg}^{-1} \)) due to its small mass.

Proton
Neutron
Alpha particle
Electron
4

The ratio of the velocities of an electron in the first orbit of \( \text{H} \) to the second orbit of \( \text{He}^+ \) is: (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \))

For \( \text{H} \) (Z = 1), \( v_1 = 2.19 \times 10^6 \, \text{m s}^{-1} \). For \( \text{He}^+ \) (Z = 2), \( v_n = \frac{Z v_1}{n} \), \( v_2 = \frac{2 \times 2.19 \times 10^6}{2} = 2.19 \times 10^6 \, \text{m s}^{-1} \). Ratio = \( \frac{2.19 \times 10^6}{2.19 \times 10^6} = 1 \).

2
0.5
4
1
4

The ionization energy of \( \text{H} \) is \( 13.6 \, \text{eV} \). What is the energy required to excite an electron in \( \text{He}^+ \) from \( n = 2 \) to \( n = 4 \)?

For \( \text{He}^+ \) (Z = 2), \( E_n = -13.6 \times Z^2 / n^2 \). \( E_2 = -13.6 \times 4 / 4 = -13.6 \, \text{eV} \), \( E_4 = -13.6 \times 4 / 16 = -3.4 \, \text{eV} \). \( \Delta E = E_4 - E_2 = -3.4 - (-13.6) = 10.2 \, \text{eV} \).

\( 13.6 \, \text{eV} \)
\( 10.2 \, \text{eV} \)
\( 40.8 \, \text{eV} \)
\( 6.8 \, \text{eV} \)
2

The ionization energy of \( \text{Be}^{3+} \) from its ground state is how many times that of a hydrogen atom? (\( E_H = 13.6 \, \text{eV} \))

For \( \text{Be}^{3+} \) (Z = 4), \( E = Z^2 E_H = 16 \times 13.6 = 217.6 \, \text{eV} \). Ratio = 16.

9
16
4
25
2

What is the wavenumber of light emitted when an electron in a hydrogen atom transitions from \( n = 4 \) to \( n = 2 \)? (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Wavenumber \( \bar{v} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{4^2} \right) = 1.097 \times 10^7 \left( \frac{1}{4} - \frac{1}{16} \right) = 2.057 \times 10^6 \, \text{m}^{-1} \).

\( 2.057 \times 10^6 \, \text{m}^{-1} \)
\( 1.5236 \times 10^6 \, \text{m}^{-1} \)
\( 3.291 \times 10^6 \, \text{m}^{-1} \)
\( 9.753 \times 10^6 \, \text{m}^{-1} \)
1

A hydrogen atom emits a photon of wavelength \( 410.2 \, \text{nm} \). What is the energy difference between the initial and final states? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

\( E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{410.2 \times 10^{-9}} = 4.847 \times 10^{-19} \, \text{J} \) (corresponds to \( n = 6 \) to \( n = 2 \) in Balmer series).

\( 3.026 \times 10^{-19} \, \text{J} \)
\( 6.626 \times 10^{-19} \, \text{J} \)
\( 4.847 \times 10^{-19} \, \text{J} \)
\( 2.423 \times 10^{-19} \, \text{J} \)
3

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