NEET Structure of Atom — Set 8

Question 1

An electron in a hydrogen atom is in the $ n = 4 $ state. How many possible sets of quantum numbers ($ n, l, m_l, m_s $) can describe its state?

Accepted Answer

For $ n = 4 $, subshells: 4s ($ l = 0 $, 1 orbital), 4p ($ l = 1 $, 3 orbitals), 4d ($ l = 2 $, 5 orbitals), 4f ($ l = 3 $, 7 orbitals). Total orbitals = $ 4^2 = 16 $. Each orbital has 2 electrons ($ m_s = +1/2, -1/2 $), so total sets = $ 16 \times 2 = 32 $.

Question 2

The ionization energy of $ \text{He}^+ $ is $ 54.4 \, \text{eV} $. What is the energy required to excite an electron from $ n = 2 $ to $ n = 5 $? ($ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} $)

Accepted Answer

For $ \text{He}^+ $ (Z = 2), $ E_n = -54.4 / n^2 $. $ E_2 = -54.4 / 4 = -13.6 \, \text{eV} $, $ E_5 = -54.4 / 25 = -2.176 \, \text{eV} $. $ \Delta E = -2.176 - (-13.6) = 11.424 \, \text{eV} = 1.828 \times 10^{-18} \, \text{J} $.

Question 3

A proton has a de Broglie wavelength of $ 2.0 \times 10^{-12} \, \text{m} $. What is its kinetic energy? ($ h = 6.626 \times 10^{-34} \, \text{J s} $, $ m_p = 1.67 \times 10^{-27} \, \text{kg} $)

Accepted Answer

$ \lambda = \frac{h}{mv} $, $ v = \frac{h}{m\lambda} = \frac{6.626 \times 10^{-34}}{1.67 \times 10^{-27} \times 2.0 \times 10^{-12}} = 1.984 \times 10^5 \, \text{m s}^{-1} $. $ KE = \frac{1}{2} m v^2 = \frac{1}{2} \times 1.67 \times 10^{-27} \times (1.984 \times 10^5)^2 = 3.29 \times 10^{-17} \, \text{J} $.

NEET Chemistry: Structure of Atom — Practice Set 8

Q1. An electron in a hydrogen atom is in the \( n = 4 \) state. How many possible sets of quantum numbers (\( n, l, m_l, m_s \)) can describe its state?

Q2. The ionization energy of \( \text{He}^+ \) is \( 54.4 \, \text{eV} \). What is the energy required to excite an electron from \( n = 2 \) to \( n = 5 \)? (\( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

Q3. A proton has a de Broglie wavelength of \( 2.0 \times 10^{-12} \, \text{m} \). What is its kinetic energy? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_p = 1.67 \times 10^{-27} \, \text{kg} \))

Q4. A neutron and a proton have the same de Broglie wavelength. What is the ratio of their velocities? (\( m_p = 1.67 \times 10^{-27} \, \text{kg} \), \( m_n = 1.67 \times 10^{-27} \, \text{kg} \))

Q5. The ionization energy of a hydrogen atom is \( 13.6 \, \text{eV} \). What is the ionization energy of \( \text{H}^- \) ion from its ground state if its electron is in \( n = 2 \)?

Q6. The maximum number of electrons in an atom with \( n = 3 \) is:

Q7. The wavelength of the second line in the Brackett series of a hydrogen atom is: (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Q8. The number of spectral lines produced when an electron falls from \( n = 7 \) to \( n = 3 \) in a hydrogen atom is:

Q9. A photon of energy \( 6.626 \times 10^{-19} \, \text{J} \) strikes a metal with a work function of \( 4.0 \times 10^{-19} \, \text{J} \). What is the velocity of the ejected electron? (\( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Q10. The de Broglie wavelength of a particle is \( 6.626 \times 10^{-10} \, \text{m} \). If its mass is \( 1.0 \times 10^{-30} \, \text{kg} \), what is its velocity? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))