NEET Structure of Atom — Set 19

Question 1

Which series of spectral lines in a hydrogen atom lies in the visible region?

Accepted Answer

The Balmer series ($ n_2 > 2 $ to $ n_1 = 2 $) lies in the visible region.

Question 2

An electron in $ \text{He}^+ $ has an angular momentum of $ 3.165 \times 10^{-34} \, \text{J s} $. What is its kinetic energy? ($ h = 6.626 \times 10^{-34} \, \text{J s} $, $ m_e = 9.1 \times 10^{-31} \, \text{kg} $)

Accepted Answer

$ L = \frac{nh}{2\pi} $, $ n = \frac{L \cdot 2\pi}{h} = \frac{3.165 \times 10^{-34} \times 2 \times 3.14}{6.626 \times 10^{-34}} = 3 $. For $ \text{He}^+ $ (Z = 2), $ v_n = \frac{Z v_1}{n} = \frac{2 \times 2.19 \times 10^6}{3} = 1.46 \times 10^6 \, \text{m s}^{-1} $. $ KE = \frac{1}{2} m v^2 = \frac{1}{2} \times 9.1 \times 10^{-31} \times (1.46 \times 10^6)^2 = 9.7 \times 10^{-19} \, \text{J} $.

Question 3

An electron in a multi-electron atom has quantum numbers $ n = 4, l = 2 $. How many possible values of $ m_l $ can it have?

Accepted Answer

For $ l = 2 $, $ m_l $ ranges from $-l$ to $+l$, i.e., -2, -1, 0, 1, 2. Total = 5 values.

NEET Chemistry: Structure of Atom — Practice Set 19

Q1. Which series of spectral lines in a hydrogen atom lies in the visible region?

Q2. An electron in \( \text{He}^+ \) has an angular momentum of \( 3.165 \times 10^{-34} \, \text{J s} \). What is its kinetic energy? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Q3. An electron in a multi-electron atom has quantum numbers \( n = 4, l = 2 \). How many possible values of \( m_l \) can it have?

Q4. The energy required to eject an electron from a metal is \( 4.5 \times 10^{-19} \, \text{J} \). If light of frequency \( 8.0 \times 10^{14} \, \text{Hz} \) is used, what is the kinetic energy of the ejected electron? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q5. The uncertainty in position of a proton is \( 5.0 \times 10^{-11} \, \text{m} \). What is the minimum uncertainty in its velocity? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_p = 1.67 \times 10^{-27} \, \text{kg} \))

Q6. The ratio of the kinetic energies of an electron in the first orbit of \( \text{Li}^{2+} \) to the second orbit of \( \text{H} \) is: (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Q7. The ratio of the radii of the second orbit of \( \text{H} \) to the first orbit of \( \text{Li}^{2+} \) is:

Q8. An element has 15 protons, 16 neutrons, and 18 electrons. What is the charge and mass number of the ion?

Q9. How many electrons in an atom can have the quantum numbers \( n = 3 \) and \( m_s = +1/2 \)?