NEET Structure of Atom — Set 10

Question 1

The ionization energy of $ \text{Li}^{2+} $ is $ 122.4 \, \text{eV} $. What is the energy required to excite an electron from $ n = 3 $ to $ n = 6 $? ($ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} $)

Accepted Answer

For $ \text{Li}^{2+} $ (Z = 3), $ E_n = -122.4 / n^2 $. $ E_3 = -122.4 / 9 = -13.6 \, \text{eV} $, $ E_6 = -122.4 / 36 = -3.4 \, \text{eV} $. $ \Delta E = -3.4 - (-13.6) = 10.2 \, \text{eV} = 1.632 \times 10^{-18} \, \text{J} $.

Question 2

The energy of an electron in the first orbit of a hydrogen atom is $ -2.18 \times 10^{-18} \, \text{J} $. What is the wavelength of the photon emitted when an electron in $ \text{Be}^{3+} $ transitions from $ n = 6 $ to $ n = 3 $? ($ h = 6.626 \times 10^{-34} \, \text{J s} $, $ c = 3.0 \times 10^8 \, \text{m s}^{-1} $)

Accepted Answer

For $ \text{Be}^{3+} $ (Z = 4), $ E_n = -Z^2 \times 2.18 \times 10^{-18} / n^2 $. $ E_3 = -16 \times 2.18 \times 10^{-18} / 9 = -3.8711 \times 10^{-18} \, \text{J} $, $ E_6 = -16 \times 2.18 \times 10^{-18} / 36 = -9.6778 \times 10^{-19} \, \text{J} $. $ \Delta E = -9.6778 \times 10^{-19} - (-3.8711 \times 10^{-18}) = 2.9033 \times 10^{-18} \, \text{J} $. $ \lambda = \frac{hc}{\Delta E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{2.9033 \times 10^{-18}} = 6.845 \times 10^{-8} \, \text{m} = 68.45 \, \text{nm} $.

Question 3

Which of the following transitions in a hydrogen atom emits light of the shortest wavelength?

Accepted Answer

Shortest wavelength (highest energy) occurs for the largest $ \Delta E $. $ n = 5 $ to $ n = 1 $ has the largest energy difference.

NEET Chemistry: Structure of Atom — Practice Set 10

Q1. The ionization energy of \( \text{Li}^{2+} \) is \( 122.4 \, \text{eV} \). What is the energy required to excite an electron from \( n = 3 \) to \( n = 6 \)? (\( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

Q3. Which of the following transitions in a hydrogen atom emits light of the shortest wavelength?

Q5. The ratio of the angular momentum of an electron in the third orbit of \( \text{H} \) to the second orbit of \( \text{He}^+ \) is: (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q6. What is the wavelength of light emitted when an electron in a hydrogen atom falls from \( n = 3 \) to \( n = 1 \)? (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

Q7. What is the angular momentum of an electron in the second Bohr orbit of a hydrogen atom? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q9. The number of spectral lines produced when an electron falls from \( n = 9 \) to \( n = 6 \) in a hydrogen atom is:

Q10. The energy required to excite an electron from \( n = 3 \) to \( n = 6 \) in a hydrogen atom is \( 1.8164 \times 10^{-19} \, \text{J} \). What is its frequency? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))