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  4. Structure of Atom Chapter-Wise Test 16

Structure of Atom Chapter-Wise Test 16

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the energy difference between \( n = 1 \) and \( n = 2 \) levels in a hydrogen atom for photon emission? (\( E_1 = -2.18 \times 10^{-18} \, \text{J} \))

For emission, \( \Delta E = |E_2 - E_1| \). \( E_2 = \frac{-2.18 \times 10^{-18}}{2^2} = -5.45 \times 10^{-19} \, \text{J} \). \( \Delta E = |-5.45 \times 10^{-19} - (-2.18 \times 10^{-18})| = 1.635 \times 10^{-18} \, \text{J} \).

A. \( 2.18 \times 10^{-18} \, \text{J} \)
B. \( 5.45 \times 10^{-19} \, \text{J} \)
C. \( 1.635 \times 10^{-18} \, \text{J} \)
D. \( 1.09 \times 10^{-18} \, \text{J} \)
3

Which of the following elements has the electronic configuration \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 \)?

Total electrons = 2 + 2 + 6 + 2 + 6 + 1 = 19, which corresponds to potassium (K).

Sodium (Na)
Calcium (Ca)
Argon (Ar)
Potassium (K)
4

How many spectral lines are observed when an electron falls from \( n = 6 \) to \( n = 3 \) in a hydrogen atom?

Transitions: 6→3, 6→4→3, 6→5→3, 5→3, 5→4→3, 4→3. Total = 6 lines.

3
4
5
6
4

What is the maximum number of electrons that can have \( n = 4 \) in an atom?

Maximum electrons = \( 2n^2 \). For \( n = 4 \), \( 2 \times 4^2 = 2 \times 16 = 32 \).

18
32
8
50
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 \( \text{C}^{5+} \) falls from \( n = 4 \) 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 \( \text{C}^{5+} \) (Z = 6), \( E_n = -13.6 \times Z^2 / n^2 \). \( E_2 = -13.6 \times 36 / 4 = -122.4 \, \text{eV} \), \( E_4 = -13.6 \times 36 / 16 = -30.6 \, \text{eV} \). \( \Delta E = -30.6 - (-122.4) = 91.8 \, \text{eV} = 1.4688 \times 10^{-17} \, \text{J} \). \( \lambda = \frac{hc}{\Delta E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{1.4688 \times 10^{-17}} = 1.353 \times 10^{-8} \, \text{m} = 13.53 \, \text{nm} \).

\( 13.53 \, \text{nm} \)
\( 27.06 \, \text{nm} \)
\( 10.20 \, \text{nm} \)
\( 17.41 \, \text{nm} \)
1

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

Lyman series: \( n_1 = 1 \), third line is \( n_2 = 4 \). \( \bar{v} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) = 1.097 \times 10^7 \left( \frac{1}{1^2} - \frac{1}{4^2} \right) = 1.097 \times 10^7 \times \frac{15}{16} = 1.028 \times 10^7 \, \text{m}^{-1} \).

\( 1.028 \times 10^7 \, \text{m}^{-1} \)
\( 9.753 \times 10^6 \, \text{m}^{-1} \)
\( 8.223 \times 10^6 \, \text{m}^{-1} \)
\( 1.097 \times 10^7 \, \text{m}^{-1} \)
1

The uncertainty in velocity of an electron is \( 1.0 \times 10^6 \, \text{m s}^{-1} \). What is the minimum uncertainty in its position? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \). \( \Delta p = m_e \Delta v = 9.1 \times 10^{-31} \times 1.0 \times 10^6 = 9.1 \times 10^{-25} \, \text{kg m s}^{-1} \). \( \Delta x \geq \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-25}} = 5.8 \times 10^{-11} \, \text{m} \).

\( 2.9 \times 10^{-11} \, \text{m} \)
\( 1.45 \times 10^{-11} \, \text{m} \)
\( 7.3 \times 10^{-11} \, \text{m} \)
\( 5.8 \times 10^{-11} \, \text{m} \)
4

The energy difference between the first and third orbits of a hydrogen atom is \( 1.936 \times 10^{-18} \, \text{J} \). What is the frequency of the photon emitted when an electron falls from \( n = 3 \) to \( n = 1 \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( E_1 = -2.18 \times 10^{-18} \, \text{J} \), \( E_3 = \frac{-2.18 \times 10^{-18}}{9} = -2.422 \times 10^{-19} \, \text{J} \). \( \Delta E = E_1 - E_3 = -2.18 \times 10^{-18} - (-2.422 \times 10^{-19}) = -1.9378 \times 10^{-18} \, \text{J} \) (emitted energy = \( 1.938 \times 10^{-18} \, \text{J} \)). \( v = \frac{\Delta E}{h} = \frac{1.938 \times 10^{-18}}{6.626 \times 10^{-34}} = 2.925 \times 10^{15} \, \text{Hz} \).

\( 2.925 \times 10^{15} \, \text{Hz} \)
\( 1.462 \times 10^{15} \, \text{Hz} \)
\( 4.387 \times 10^{15} \, \text{Hz} \)
\( 3.291 \times 10^{15} \, \text{Hz} \)
1

A metal has a threshold frequency of \( 6.0 \times 10^{14} \, \text{Hz} \). What is the kinetic energy of an electron ejected by light of frequency \( 9.0 \times 10^{14} \, \text{Hz} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( W_0 = h v_0 = 6.626 \times 10^{-34} \times 6.0 \times 10^{14} = 3.9756 \times 10^{-19} \, \text{J} \). \( E = h v = 6.626 \times 10^{-34} \times 9.0 \times 10^{14} = 5.9634 \times 10^{-19} \, \text{J} \). \( KE = E - W_0 = 5.9634 \times 10^{-19} - 3.9756 \times 10^{-19} = 1.9878 \times 10^{-19} \, \text{J} \).

\( 3.9756 \times 10^{-19} \, \text{J} \)
\( 1.9878 \times 10^{-19} \, \text{J} \)
\( 5.9634 \times 10^{-19} \, \text{J} \)
\( 2.6504 \times 10^{-19} \, \text{J} \)
2

How many possible values of \( m_l \) are there for an electron with \( n = 5 \) and \( l = 4 \)?

For \( l = 4 \), \( m_l = -4, -3, -2, -1, 0, +1, +2, +3, +4 \). Total = \( 2l + 1 = 2 \times 4 + 1 = 9 \).

7
5
9
11
3

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