NEET Structure of Atom — Set 1

Question 1

The ratio of the velocities of an electron in the second orbit of $ \text{H} $ to the third orbit of $ \text{Li}^{2+} $ is: ($ v_1 $ for H = $ 2.19 \times 10^6 \, \text{m s}^{-1} $)

Accepted Answer

For $ \text{H} $ (Z = 1), $ v_2 = 2.19 \times 10^6 / 2 = 1.095 \times 10^6 \, \text{m s}^{-1} $. For $ \text{Li}^{2+} $ (Z = 3), $ v_3 = 3 \times 2.19 \times 10^6 / 3 = 2.19 \times 10^6 \, \text{m s}^{-1} $. Ratio = $ 1.095 \times 10^6 / 2.19 \times 10^6 = 0.5 $.

Question 2

The de Broglie wavelength of an electron is $ 5.0 \times 10^{-10} \, \text{m} $ and its kinetic energy is $ 3.026 \times 10^{-19} \, \text{J} $. What is the uncertainty in its position? ($ h = 6.626 \times 10^{-34} \, \text{J s} $)

Accepted Answer

Momentum $ p = \frac{h}{\lambda} = \frac{6.626 \times 10^{-34}}{5.0 \times 10^{-10}} = 1.3252 \times 10^{-24} \, \text{kg m s}^{-1} $. $ \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 1.3252 \times 10^{-24}} = 3.98 \times 10^{-11} \, \text{m} $.

Question 3

How many electrons in an atom can have the quantum numbers $ n = 6 $ and $ l = 4 $?

Accepted Answer

For $ l = 4 $ (g subshell), orbitals = $ 2l + 1 = 9 $. Electrons = $ 9 \times 2 = 18 $.

NEET Chemistry: Structure of Atom — Practice Set 1

Q1. The ratio of the velocities of an electron in the second orbit of \( \text{H} \) to the third orbit of \( \text{Li}^{2+} \) is: (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \))

Q2. The de Broglie wavelength of an electron is \( 5.0 \times 10^{-10} \, \text{m} \) and its kinetic energy is \( 3.026 \times 10^{-19} \, \text{J} \). What is the uncertainty in its position? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q3. How many electrons in an atom can have the quantum numbers \( n = 6 \) and \( l = 4 \)?

Q4. The wavelength of the fifth line in the Pfund series of a hydrogen atom is: (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Q5. The ratio of the wavelengths of the second lines in the Balmer and Paschen series of a hydrogen atom is: (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Q6. The radius of the first Bohr orbit of \( \text{He}^+ \) is \( 2.645 \times 10^{-11} \, \text{m} \). What is the radius of the third orbit of \( \text{Li}^{2+} \) if the Bohr radius for hydrogen is \( 5.29 \times 10^{-11} \, \text{m} \)?

Q7. The threshold frequency of a metal is \( 5.0 \times 10^{14} \, \text{Hz} \). What is its work function in eV? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

Q8. An electron in \( \text{He}^+ \) transitions from \( n = 3 \) to \( n = 1 \). What is the wavelength of the emitted photon in nm? (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

Q9. An electron has a de Broglie wavelength of \( 2.0 \times 10^{-10} \, \text{m} \). What is its kinetic energy in joules? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Q10. What is the frequency of light emitted when an electron in \( \text{He}^+ \) transitions from \( n = 2 \) to \( n = 1 \)? (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))