Structure of Atom Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The uncertainty in momentum of a neutron is \( 5.0 \times 10^{-25} \, \text{kg m s}^{-1} \). What is the minimum uncertainty in its position? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \), \( \Delta x \geq \frac{h}{4\pi \Delta p} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 5.0 \times 10^{-25}} = 1.055 \times 10^{-10} \, \text{m} \).

\( 5.27 \times 10^{-11} \, \text{m} \)
\( 2.64 \times 10^{-10} \, \text{m} \)
\( 1.055 \times 10^{-10} \, \text{m} \)
\( 3.31 \times 10^{-10} \, \text{m} \)
3

The radius of the third orbit of a hydrogen atom is \( 4.761 \times 10^{-10} \, \text{m} \). What is the angular momentum of an electron in the fifth orbit? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( r_1 \) for H = \( 5.29 \times 10^{-11} \, \text{m} \))

\( r_3 = 9 \times 5.29 \times 10^{-11} = 4.761 \times 10^{-10} \, \text{m} \). \( L = \frac{nh}{2\pi} \), for \( n = 5 \), \( L = \frac{5 \times 6.626 \times 10^{-34}}{2 \times 3.14} = 5.275 \times 10^{-34} \, \text{J s} \).

\( 5.275 \times 10^{-34} \, \text{J s} \)
\( 3.165 \times 10^{-34} \, \text{J s} \)
\( 6.33 \times 10^{-34} \, \text{J s} \)
\( 2.11 \times 10^{-34} \, \text{J s} \)
1

The angular momentum of an electron in the fifth orbit of \( \text{Be}^{3+} \) is \( 5.275 \times 10^{-34} \, \text{J s} \). What is its radius? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( r_1 \) for H = \( 5.29 \times 10^{-11} \, \text{m} \))

\( L = \frac{nh}{2\pi} \), \( n = \frac{L \cdot 2\pi}{h} = \frac{5.275 \times 10^{-34} \times 2 \times 3.14}{6.626 \times 10^{-34}} = 5 \). For \( \text{Be}^{3+} \) (Z = 4), \( r_n = \frac{n^2}{Z} r_1 = \frac{5^2}{4} \times 5.29 \times 10^{-11} = 6.25 \times 5.29 \times 10^{-11} = 3.306 \times 10^{-10} \, \text{m} \).

\( 3.306 \times 10^{-10} \, \text{m} \)
\( 1.322 \times 10^{-10} \, \text{m} \)
\( 5.29 \times 10^{-11} \, \text{m} \)
\( 2.645 \times 10^{-11} \, \text{m} \)
1

The work function of a metal is \( 3.31 \times 10^{-19} \, \text{J} \). What is the threshold wavelength in nm? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

\( W_0 = \frac{hc}{\lambda_0} \), so \( \lambda_0 = \frac{hc}{W_0} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{3.31 \times 10^{-19}} = 6.0 \times 10^{-7} \, \text{m} = 600 \, \text{nm} \).

\( 400 \, \text{nm} \)
\( 600 \, \text{nm} \)
\( 300 \, \text{nm} \)
\( 800 \, \text{nm} \)
2

How many protons, neutrons, and electrons are present in the neutral atom with atomic number 35 and mass number 80?

For a neutral atom, protons = electrons = atomic number = 35. Neutrons = mass number - atomic number = 80 - 35 = 45.

35 protons, 45 neutrons, 35 electrons
45 protons, 35 neutrons, 45 electrons
35 protons, 80 neutrons, 35 electrons
80 protons, 35 neutrons, 80 electrons
1

A proton and an electron have the same kinetic energy. What is the ratio of their de Broglie wavelengths? (\( m_p = 1.67 \times 10^{-27} \, \text{kg} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

De Broglie wavelength \( \lambda = \frac{h}{\sqrt{2mKE}} \). For equal KE, \( \lambda_p / \lambda_e = \sqrt{m_e / m_p} = \sqrt{9.1 \times 10^{-31} / 1.67 \times 10^{-27}} \approx \sqrt{5.45 \times 10^{-4}} \approx 0.0233 \).

A. 0.0122
B. 0.0233
C. 0.0466
D. 1.000
2

What is the frequency of electromagnetic radiation with a wavelength of 600 nm? (Speed of light \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

Frequency \( v = \frac{c}{\lambda} = \frac{3.0 \times 10^8}{600 \times 10^{-9}} = 5.0 \times 10^{14} \, \text{Hz} \).

\(5.0 \times 10^{14} \, \text{Hz}\)
\(6.0 \times 10^{14} \, \text{Hz}\)
\(4.0 \times 10^{14} \, \text{Hz}\)
\(3.0 \times 10^{14} \, \text{Hz}\)
1

The ratio of the angular momentum of an electron in the fifth orbit of \( \text{H} \) to the third orbit of \( \text{He}^+ \) is: (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

For \( \text{H} \) (Z = 1), \( L_5 = 5h / 2\pi \). For \( \text{He}^+ \) (Z = 2), \( L_3 = 3h / 2\pi \). Ratio = \( (5h / 2\pi) / (3h / 2\pi) = 5/3 \approx 1.667 \).

\( 0.6 \)
\( 2.5 \)
\( 1.0 \)
\( 1.667 \)
4

The work function of a metal is \( 2.5 \, \text{eV} \). What is the maximum wavelength of light that can eject electrons from this metal? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

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

\( 620 \, \text{nm} \)
\( 400 \, \text{nm} \)
\( 331 \, \text{nm} \)
\( 497 \, \text{nm} \)
4

How many electrons can occupy the \( 4d \) subshell?

For \( l = 2 \) (d subshell), number of orbitals = \( 2l + 1 = 5 \). Electrons = \( 5 \times 2 = 10 \).

6
2
10
14
3

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