NEET Structure of Atom — Set 5

Question 1

The uncertainty in velocity of an electron is $ 1.0 \times 10^6 \, \text{m s}^{-1} $. What is the minimum uncertainty in its position? ($ h = 6.626 \times 10^{-34} \, \text{J s} $, $ m_e = 9.1 \times 10^{-31} \, \text{kg} $)

Accepted Answer

$ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} $. $ \Delta p = m_e \Delta v = 9.1 \times 10^{-31} \times 1.0 \times 10^6 = 9.1 \times 10^{-25} \, \text{kg m s}^{-1} $. $ \Delta x \geq \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-25}} = 5.8 \times 10^{-11} \, \text{m} $.

Question 2

How many spectral lines are observed when an electron falls from $ n = 6 $ to $ n = 3 $ in a hydrogen atom?

Accepted Answer

Transitions: 6→3, 6→4→3, 6→5→3, 5→3, 5→4→3, 4→3. Total = 6 lines.

Question 3

The wavenumber of the third line in the Lyman series of a hydrogen atom is: ($ R_H = 1.097 \times 10^7 \, \text{m}^{-1} $)

Accepted Answer

Lyman series: $ n_1 = 1 $, third line is $ n_2 = 4 $. $ \bar{v} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) = 1.097 \times 10^7 \left( \frac{1}{1^2} - \frac{1}{4^2} \right) = 1.097 \times 10^7 \times \frac{15}{16} = 1.028 \times 10^7 \, \text{m}^{-1} $.

NEET Chemistry: Structure of Atom — Practice Set 5

Q1. The uncertainty in velocity of an electron is \( 1.0 \times 10^6 \, \text{m s}^{-1} \). What is the minimum uncertainty in its position? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Q2. How many spectral lines are observed when an electron falls from \( n = 6 \) to \( n = 3 \) in a hydrogen atom?

Q3. The wavenumber of the third line in the Lyman series of a hydrogen atom is: (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Q4. What is the maximum number of electrons that can have \( n = 4 \) in an atom?

Q5. How many possible values of \( m_l \) are there for an electron with \( n = 5 \) and \( l = 4 \)?

Q6. A metal has a threshold frequency of \( 6.0 \times 10^{14} \, \text{Hz} \). What is the kinetic energy of an electron ejected by light of frequency \( 9.0 \times 10^{14} \, \text{Hz} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q7. What is the energy difference between \( n = 1 \) and \( n = 2 \) levels in a hydrogen atom for photon emission? (\( E_1 = -2.18 \times 10^{-18} \, \text{J} \))

Q8. The energy difference between the first and third orbits of a hydrogen atom is \( 1.936 \times 10^{-18} \, \text{J} \). What is the frequency of the photon emitted when an electron falls from \( n = 3 \) to \( n = 1 \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q9. Which of the following elements has the electronic configuration \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 \)?