Structure of Atom Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The kinetic energy of a photoelectron is \( 3.0 \times 10^{-19} \, \text{J} \) when irradiated with light of frequency \( 8.0 \times 10^{14} \, \text{Hz} \). What is the threshold frequency of the metal? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Photon energy \( E = h v = 6.626 \times 10^{-34} \times 8.0 \times 10^{14} = 5.3008 \times 10^{-19} \, \text{J} \). \( W_0 = E - KE = 5.3008 \times 10^{-19} - 3.0 \times 10^{-19} = 2.3008 \times 10^{-19} \, \text{J} \). \( v_0 = \frac{W_0}{h} = \frac{2.3008 \times 10^{-19}}{6.626 \times 10^{-34}} = 3.47 \times 10^{14} \, \text{Hz} \).

\( 5.0 \times 10^{14} \, \text{Hz} \)
\( 3.47 \times 10^{14} \, \text{Hz} \)
\( 8.0 \times 10^{14} \, \text{Hz} \)
\( 4.53 \times 10^{14} \, \text{Hz} \)
2

In a hydrogen atom, the energy of an electron in the first orbit is \(-2.18 \times 10^{-18} \, \text{J}\). What is the energy of the electron in the third orbit?

Energy \( E_n = \frac{-2.18 \times 10^{-18}}{n^2} \). For \( n = 3 \), \( E_3 = \frac{-2.18 \times 10^{-18}}{9} = -2.4222 \times 10^{-19} \, \text{J} \).

\(-2.4222 \times 10^{-19} \, \text{J}\)
\(-5.45 \times 10^{-19} \, \text{J}\)
\(-1.09 \times 10^{-18} \, \text{J}\)
\(-2.18 \times 10^{-18} \, \text{J}\)
1

What is the maximum number of orbitals in the \( n = 2 \) energy level?

Number of orbitals = \( n^2 \). For \( n = 2 \), \( 2^2 = 4 \) (2s: 1, 2p: 3).

A. 2
B. 4
C. 8
D. 6
2

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

Paschen series: \( n_1 = 3 \), second line is \( n_2 = 5 \). \( \bar{v} = 1.097 \times 10^7 (1/9 - 1/25) = 1.097 \times 10^7 \times 16/225 = 7.805 \times 10^5 \, \text{m}^{-1} \).

\( 7.805 \times 10^5 \, \text{m}^{-1} \)
\( 5.33 \times 10^5 \, \text{m}^{-1} \)
\( 3.81 \times 10^5 \, \text{m}^{-1} \)
\( 9.12 \times 10^5 \, \text{m}^{-1} \)
1

An atom has the electronic configuration \( 1s^2 2s^2 2p^6 3s^2 3p^5 \). What is its atomic number?

Total electrons = 2 + 2 + 6 + 2 + 5 = 17. Atomic number = 17.

15
17
16
18
2

The uncertainty in momentum of an electron is \( 1.0 \times 10^{-24} \, \text{kg m s}^{-1} \). What is the minimum uncertainty in its position? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \). \( \Delta x \geq \frac{h}{4\pi \Delta p} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 1.0 \times 10^{-24}} = 5.27 \times 10^{-11} \, \text{m} \).

\( 2.63 \times 10^{-11} \, \text{m} \)
\( 1.32 \times 10^{-10} \, \text{m} \)
\( 5.27 \times 10^{-11} \, \text{m} \)
\( 6.62 \times 10^{-10} \, \text{m} \)
3

An atom has an electronic configuration of \( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^1 \). What is its atomic number?

Total electrons = 2 + 2 + 6 + 2 + 6 + 10 + 1 = 29. Atomic number = 29.

28
30
29
27
3

How many possible sets of quantum numbers (\( n, l, m_l, m_s \)) are there for electrons in the \( n = 3 \) energy level?

For \( n = 3 \), orbitals = \( 3^2 = 9 \) (3s: 1, 3p: 3, 3d: 5). Each orbital has 2 electrons (\( m_s = +1/2, -1/2 \)), total sets = \( 9 \times 2 = 18 \).

9
12
18
6
3

A photon of wavelength 300 nm strikes a metal surface, and the ejected electron has a kinetic energy of \( 2.0 \times 10^{-19} \, \text{J} \). What is the work function of the metal? (\( h = 6.626 \times 10^{-34} \, \text{J s}, c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

Photon energy \( E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{300 \times 10^{-9}} = 6.626 \times 10^{-19} \, \text{J} \). Work function \( W_0 = E - KE = 6.626 \times 10^{-19} - 2.0 \times 10^{-19} = 4.626 \times 10^{-19} \, \text{J} \).

\(2.0 \times 10^{-19} \, \text{J}\)
\(6.626 \times 10^{-19} \, \text{J}\)
\(3.313 \times 10^{-19} \, \text{J}\)
\(4.626 \times 10^{-19} \, \text{J}\)
4

The number of spectral lines produced when an electron falls from \( n = 8 \) to \( n = 5 \) in a hydrogen atom is:

Number of spectral lines = \( \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2} = \frac{(8 - 5)(8 - 5 + 1)}{2} = 6 \). Transitions: 8→5, 8→6, 8→7, 7→5, 7→6, 6→5.

A. 4
B. 6
C. 3
D. 5
2

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