Structure of Atom Chapter-Wise Test 19

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The ratio of the kinetic energies of an electron in the first orbit of \( \text{Li}^{2+} \) to the second orbit of \( \text{H} \) is: (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

For \( \text{Li}^{2+} \) (Z = 3), \( v_1 = 3 \times 2.19 \times 10^6 = 6.57 \times 10^6 \, \text{m s}^{-1} \), \( KE_1 = \frac{1}{2} \times 9.1 \times 10^{-31} \times (6.57 \times 10^6)^2 = 1.962 \times 10^{-17} \, \text{J} \). For \( \text{H} \) (Z = 1), \( v_2 = 2.19 \times 10^6 / 2 = 1.095 \times 10^6 \, \text{m s}^{-1} \), \( KE_2 = 2.18 \times 10^{-18} \, \text{J} \). Ratio = \( 1.962 \times 10^{-17} / 2.18 \times 10^{-18} = 9 \).

\( 3 \)
\( 6 \)
\( 12 \)
\( 9 \)
4

Which series of spectral lines in a hydrogen atom lies in the visible region?

The Balmer series (\( n_2 > 2 \) to \( n_1 = 2 \)) lies in the visible region.

Lyman series
Paschen series
Balmer series
Brackett series
3

An electron in a multi-electron atom has quantum numbers \( n = 4, l = 2 \). How many possible values of \( m_l \) can it have?

For \( l = 2 \), \( m_l \) ranges from \(-l\) to \(+l\), i.e., -2, -1, 0, 1, 2. Total = 5 values.

3
7
4
5
4

An element has 15 protons, 16 neutrons, and 18 electrons. What is the charge and mass number of the ion?

Charge = protons - electrons = 15 - 18 = -3. Mass number = protons + neutrons = 15 + 16 = 31.

\( +3, 31 \)
\( -1, 33 \)
\( +1, 31 \)
\( -3, 31 \)
4

The uncertainty in position of a proton is \( 5.0 \times 10^{-11} \, \text{m} \). What is the minimum uncertainty in its velocity? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_p = 1.67 \times 10^{-27} \, \text{kg} \))

\( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \). \( \Delta v \geq \frac{h}{4\pi m_p \Delta x} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 1.67 \times 10^{-27} \times 5.0 \times 10^{-11}} = 6.3 \times 10^2 \, \text{m s}^{-1} \).

\( 3.15 \times 10^2 \, \text{m s}^{-1} \)
\( 1.26 \times 10^3 \, \text{m s}^{-1} \)
\( 6.3 \times 10^2 \, \text{m s}^{-1} \)
\( 9.45 \times 10^2 \, \text{m s}^{-1} \)
3

How many electrons in an atom can have the quantum numbers \( n = 3 \) and \( m_s = +1/2 \)?

For \( n = 3 \), orbitals = \( 3^2 = 9 \) (3s: 1, 3p: 3, 3d: 5). Each orbital holds 2 electrons, total = 18. Half have \( m_s = +1/2 \), so \( 18 / 2 = 9 \).

18
9
6
12
2

An electron in \( \text{He}^+ \) has an angular momentum of \( 3.165 \times 10^{-34} \, \text{J s} \). What is its kinetic energy? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( L = \frac{nh}{2\pi} \), \( n = \frac{L \cdot 2\pi}{h} = \frac{3.165 \times 10^{-34} \times 2 \times 3.14}{6.626 \times 10^{-34}} = 3 \). For \( \text{He}^+ \) (Z = 2), \( v_n = \frac{Z v_1}{n} = \frac{2 \times 2.19 \times 10^6}{3} = 1.46 \times 10^6 \, \text{m s}^{-1} \). \( KE = \frac{1}{2} m v^2 = \frac{1}{2} \times 9.1 \times 10^{-31} \times (1.46 \times 10^6)^2 = 9.7 \times 10^{-19} \, \text{J} \).

\( 2.18 \times 10^{-18} \, \text{J} \)
\( 4.85 \times 10^{-19} \, \text{J} \)
\( 1.94 \times 10^{-18} \, \text{J} \)
\( 9.7 \times 10^{-19} \, \text{J} \)
4

The ratio of the radii of the second orbit of \( \text{H} \) to the first orbit of \( \text{Li}^{2+} \) is:

For \( \text{H} \) (Z = 1), \( r_2 = 2^2 \times r_1 = 4r_1 \). For \( \text{Li}^{2+} \) (Z = 3), \( r_1 = \frac{1^2}{3} r_1 = \frac{r_1}{3} \). Ratio = \( \frac{4r_1}{r_1 / 3} = 4 \times 3 = 12 \).

4
12
6
8
2

The energy required to eject an electron from a metal is \( 4.5 \times 10^{-19} \, \text{J} \). If light of frequency \( 8.0 \times 10^{14} \, \text{Hz} \) is used, what is the kinetic energy of the ejected electron? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Photon energy \( E = h v = 6.626 \times 10^{-34} \times 8.0 \times 10^{14} = 5.3008 \times 10^{-19} \, \text{J} \). Kinetic energy \( KE = E - W_0 = 5.3008 \times 10^{-19} - 4.5 \times 10^{-19} = 8.008 \times 10^{-20} \, \text{J} \).

\( 4.5 \times 10^{-19} \, \text{J} \)
\( 5.3008 \times 10^{-19} \, \text{J} \)
\( 1.3252 \times 10^{-19} \, \text{J} \)
\( 8.008 \times 10^{-20} \, \text{J} \)
4

A metal has a work function of \( 3.0 \, \text{eV} \). What is the stopping potential when irradiated with light of wavelength \( 300 \, \text{nm} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( e = 1.6 \times 10^{-19} \, \text{C} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

\( E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{300 \times 10^{-9}} = 6.626 \times 10^{-19} \, \text{J} = 4.141 \, \text{eV} \). \( W_0 = 3.0 \, \text{eV} \). \( KE = 4.141 - 3.0 = 1.141 \, \text{eV} \). \( V_s = \frac{KE}{e} = 1.141 \, \text{V} \).

\( 2.5 \, \text{V} \)
\( 0.5 \, \text{V} \)
\( 4.14 \, \text{V} \)
\( 1.14 \, \text{V} \)
4

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