Structure of Atom Chapter-Wise Test 18

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The frequency of a photon is \( 7.5 \times 10^{14} \, \text{Hz} \). What is its energy in joules? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Energy \( E = h v = 6.626 \times 10^{-34} \times 7.5 \times 10^{14} = 4.9695 \times 10^{-19} \, \text{J} \).

\( 4.9695 \times 10^{-19} \, \text{J} \)
\( 3.313 \times 10^{-19} \, \text{J} \)
\( 6.626 \times 10^{-19} \, \text{J} \)
\( 2.48475 \times 10^{-19} \, \text{J} \)
1

An electron in a hydrogen atom is excited to \( n = 4 \). How many possible emission lines can it produce?

Number of lines = \( \frac{n(n-1)}{2} = \frac{4 \times 3}{2} = 6 \) (4→3, 4→2, 4→1, 3→2, 3→1, 2→1).

4
5
6
3
3

Which of the following has the same number of neutrons as an atom with 12 protons and mass number 24?

Neutrons = 24 - 12 = 12. For \( ^{23}_{11}\text{Na} \), neutrons = 23 - 11 = 12.

\( ^{25}_{12}\text{Mg} \)
\( ^{24}_{13}\text{Al} \)
\( ^{23}_{11}\text{Na} \)
\( ^{26}_{14}\text{Si} \)
3

A metal has a work function of \( 3.2 \, \text{eV} \). What is the kinetic energy of an electron ejected by light of wavelength \( 350 \, \text{nm} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

\( E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{350 \times 10^{-9}} = 5.6794 \times 10^{-19} \, \text{J} = 3.5496 \, \text{eV} \). \( W_0 = 3.2 \, \text{eV} \). \( KE = 3.5496 - 3.2 = 0.3496 \, \text{eV} = 5.5936 \times 10^{-20} \, \text{J} \).

\( 5.6794 \times 10^{-19} \, \text{J} \)
\( 5.5936 \times 10^{-20} \, \text{J} \)
\( 2.0858 \times 10^{-19} \, \text{J} \)
\( 3.9756 \times 10^{-19} \, \text{J} \)
2

The energy of an electron in the second orbit of a hydrogen atom is \( -5.45 \times 10^{-19} \, \text{J} \). What is its energy in the fourth orbit?

For hydrogen, \( E_n = \frac{-2.18 \times 10^{-18}}{n^2} \). Given \( E_2 = -5.45 \times 10^{-19} \, \text{J} \) for \( n = 2 \), for \( n = 4 \), \( E_4 = \frac{-2.18 \times 10^{-18}}{4^2} = -1.3625 \times 10^{-19} \, \text{J} \).

\( -1.3625 \times 10^{-19} \, \text{J} \)
\( -2.725 \times 10^{-19} \, \text{J} \)
\( -5.45 \times 10^{-19} \, \text{J} \)
\( -8.72 \times 10^{-19} \, \text{J} \)
1

The ionization energy of \( \text{Li}^{2+} \) is \( 122.4 \, \text{eV} \). What is the wavelength of light required to excite an electron from \( n = 1 \) to \( n = 3 \) in \( \text{Li}^{2+} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

For \( \text{Li}^{2+} \) (Z = 3), \( E_n = -122.4 / n^2 \). \( E_1 = -122.4 \, \text{eV} \), \( E_3 = -122.4 / 9 = -13.6 \, \text{eV} \). \( \Delta E = -13.6 - (-122.4) = 108.8 \, \text{eV} = 1.741 \times 10^{-17} \, \text{J} \). \( \lambda = \frac{hc}{\Delta E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{1.741 \times 10^{-17}} = 1.142 \times 10^{-8} \, \text{m} = 11.42 \, \text{nm} \).

\( 9.11 \, \text{nm} \)
\( 13.6 \, \text{nm} \)
\( 11.42 \, \text{nm} \)
\( 15.2 \, \text{nm} \)
3

Which of the following radiations has the highest frequency?

Frequency increases as wavelength decreases. Gamma rays have the shortest wavelength, hence highest frequency.

Microwaves
Visible light
X-rays
Gamma rays
4

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

\( KE = \frac{1}{2} m v^2 \). For \( \text{H} \), \( v_1 = 2.19 \times 10^6 \), \( KE_1 = \frac{1}{2} \times 9.1 \times 10^{-31} \times (2.19 \times 10^6)^2 = 2.18 \times 10^{-18} \, \text{J} \). For \( \text{He}^+ \) (Z = 2), \( v_2 = \frac{2 \times 2.19 \times 10^6}{2} = 2.19 \times 10^6 \), \( KE_2 = 2.18 \times 10^{-18} \, \text{J} \). Ratio = 1.

0.5
2
4
1
4

The uncertainty in velocity of a proton is \( 2.0 \times 10^5 \, \text{m s}^{-1} \). What is the minimum uncertainty in its position? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_p = 1.67 \times 10^{-27} \, \text{kg} \))

\( \Delta p = m_p \Delta v = 1.67 \times 10^{-27} \times 2.0 \times 10^5 = 3.34 \times 10^{-22} \, \text{kg m s}^{-1} \). \( \Delta x \geq \frac{h}{4\pi \Delta p} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 3.34 \times 10^{-22}} = 1.58 \times 10^{-13} \, \text{m} \).

\( 3.16 \times 10^{-13} \, \text{m} \)
\( 7.9 \times 10^{-14} \, \text{m} \)
\( 5.27 \times 10^{-13} \, \text{m} \)
\( 1.58 \times 10^{-13} \, \text{m} \)
4

The uncertainty in position of an electron is \( 2.0 \times 10^{-10} \, \text{m} \). What is the minimum uncertainty in its momentum? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

\( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \), \( \Delta p \geq \frac{h}{4\pi \Delta x} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 2.0 \times 10^{-10}} = 2.64 \times 10^{-25} \, \text{kg m s}^{-1} \).

\( 1.32 \times 10^{-25} \, \text{kg m s}^{-1} \)
\( 5.27 \times 10^{-25} \, \text{kg m s}^{-1} \)
\( 2.64 \times 10^{-25} \, \text{kg m s}^{-1} \)
\( 3.31 \times 10^{-25} \, \text{kg m s}^{-1} \)
3

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