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  4. Structure of Atom Chapter-Wise Test 6

Structure of Atom Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A photon of energy \( 5.0 \times 10^{-19} \, \text{J} \) strikes a metal with a work function of \( 3.5 \times 10^{-19} \, \text{J} \). What is the velocity of the ejected electron? (\( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( KE = E - W_0 = 5.0 \times 10^{-19} - 3.5 \times 10^{-19} = 1.5 \times 10^{-19} \, \text{J} \). \( KE = \frac{1}{2} m v^2 \), \( v = \sqrt{\frac{2 \times 1.5 \times 10^{-19}}{9.1 \times 10^{-31}}} = \sqrt{3.297 \times 10^{11}} = 5.74 \times 10^5 \, \text{m s}^{-1} \).

\( 5.74 \times 10^5 \, \text{m s}^{-1} \)
\( 8.12 \times 10^5 \, \text{m s}^{-1} \)
\( 4.06 \times 10^5 \, \text{m s}^{-1} \)
\( 1.095 \times 10^6 \, \text{m s}^{-1} \)
1

Which set of quantum numbers is not possible for an electron?

For \( n = 1 \), \( l \) can be 0 only (not 1). Thus, \( n = 1, l = 1 \) is not possible.

\( n = 2, l = 1, m_l = 0, m_s = +1/2 \)
\( n = 3, l = 0, m_l = 0, m_s = -1/2 \)
\( n = 1, l = 1, m_l = 0, m_s = +1/2 \)
\( n = 4, l = 2, m_l = -2, m_s = -1/2 \)
3

The radius of the first Bohr orbit of a hydrogen atom is \( 5.29 \times 10^{-11} \, \text{m} \). What is the radius of the second Bohr orbit?

Radius \( r_n = r_1 \times n^2 \). For \( n = 2 \), \( r_2 = 5.29 \times 10^{-11} \times 4 = 2.116 \times 10^{-10} \, \text{m} \).

\( 2.116 \times 10^{-10} \, \text{m} \)
\( 1.058 \times 10^{-10} \, \text{m} \)
\( 5.29 \times 10^{-11} \, \text{m} \)
\( 4.232 \times 10^{-10} \, \text{m} \)
1

What is the de Broglie wavelength of an electron moving with a velocity of \( 2.0 \times 10^6 \, \text{m s}^{-1} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Wavelength \( \lambda = \frac{h}{m v} = \frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 2.0 \times 10^6} = 3.64 \times 10^{-10} \, \text{m} \).

\(1.82 \times 10^{-10} \, \text{m}\)
\(3.64 \times 10^{-10} \, \text{m}\)
\(5.46 \times 10^{-10} \, \text{m}\)
\(7.28 \times 10^{-10} \, \text{m}\)
2

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

Pfund series: \( n_1 = 5 \), third line is \( n_2 = 8 \). \( \bar{v} = 1.097 \times 10^7 (1/25 - 1/64) = 1.097 \times 10^7 \times 39/1600 = 2.673 \times 10^5 \, \text{m}^{-1} \). \( \lambda = 1 / \bar{v} = 3.741 \times 10^{-6} \, \text{m} = 3741 \, \text{nm} \).

\( 4654 \, \text{nm} \)
\( 2279 \, \text{nm} \)
\( 3741 \, \text{nm} \)
\( 1876 \, \text{nm} \)
3

The threshold wavelength of a metal is \( 500 \, \text{nm} \). What is its work function in joules? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

\( W_0 = \frac{hc}{\lambda_0} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{500 \times 10^{-9}} = 3.9756 \times 10^{-19} \, \text{J} \).

\( 6.626 \times 10^{-19} \, \text{J} \)
\( 3.9756 \times 10^{-19} \, \text{J} \)
\( 2.6504 \times 10^{-19} \, \text{J} \)
\( 1.9878 \times 10^{-19} \, \text{J} \)
2

Which of the following particles has the longest de Broglie wavelength if all have the same velocity?

\( \lambda = \frac{h}{mv} \). Wavelength is inversely proportional to mass. Electron has the smallest mass, hence longest wavelength.

Proton
Neutron
Alpha particle
Electron
4

The kinetic energy of an electron in the third orbit of \( \text{Be}^{3+} \) is \( 2.42 \times 10^{-18} \, \text{J} \). What is its velocity? (\( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

\( KE = \frac{1}{2} m v^2 \), \( v = \sqrt{\frac{2 \times 2.42 \times 10^{-18}}{9.1 \times 10^{-31}}} = \sqrt{5.319 \times 10^{12}} = 2.306 \times 10^6 \, \text{m s}^{-1} \).

\( 2.19 \times 10^6 \, \text{m s}^{-1} \)
\( 1.095 \times 10^6 \, \text{m s}^{-1} \)
\( 2.306 \times 10^6 \, \text{m s}^{-1} \)
\( 4.38 \times 10^6 \, \text{m s}^{-1} \)
3

The angular momentum of an electron in the fourth orbit of a hydrogen atom is \( 4.22 \times 10^{-34} \, \text{J s} \). What is its energy in eV? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

\( L = \frac{nh}{2\pi} \). \( n = \frac{L \cdot 2\pi}{h} = \frac{4.22 \times 10^{-34} \times 2 \times 3.14}{6.626 \times 10^{-34}} = 4 \). \( E_n = \frac{-13.6}{n^2} = \frac{-13.6}{16} = -0.85 \, \text{eV} \).

\( -3.4 \, \text{eV} \)
\( -1.51 \, \text{eV} \)
\( -13.6 \, \text{eV} \)
\( -0.85 \, \text{eV} \)
4

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

\( \lambda = \frac{h}{\sqrt{2mKE}} \). For equal \( \lambda \), \( \sqrt{2m_e KE_e} = \sqrt{2m_p KE_p} \). \( KE_e / KE_p = m_p / m_e = 1.67 \times 10^{-27} / 9.1 \times 10^{-31} \approx 1836 \).

1
1836
918
0.00054
2

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