NEET Structure of Atom — Set 12

Question 1

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

Accepted Answer

Heisenberg’s principle: $ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} $. $ \Delta p = m_e \Delta v $, so $ \Delta v \geq \frac{h}{4\pi m_e \Delta x} = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 1.0 \times 10^{-10}} = 5.8 \times 10^5 \, \text{m s}^{-1} $.

Question 2

A photon has an energy of $ 4.968 \times 10^{-19} \, \text{J} $. What is its wavelength in nanometers? ($ h = 6.626 \times 10^{-34} \, \text{J s} $, $ c = 3.0 \times 10^8 \, \text{m s}^{-1} $)

Accepted Answer

$ E = \frac{hc}{\lambda} $, so $ \lambda = \frac{hc}{E} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{4.968 \times 10^{-19}} = 4.0 \times 10^{-7} \, \text{m} = 400 \, \text{nm} $.

Question 3

How many spectral lines are observed when an electron falls from $ n = 4 $ to $ n = 2 $ in a hydrogen atom?

Accepted Answer

Transitions: 4→2, 4→3→2, 3→2. Total lines = 3.

NEET Chemistry: Structure of Atom — Practice Set 12

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

Q2. A photon has an energy of \( 4.968 \times 10^{-19} \, \text{J} \). What is its wavelength in nanometers? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

Q3. How many spectral lines are observed when an electron falls from \( n = 4 \) to \( n = 2 \) in a hydrogen atom?

Q4. An electron in \( \text{Li}^{2+} \) is in the \( n = 2 \) state. What is its energy in joules? (\( E_1 \) for H = \( -2.18 \times 10^{-18} \, \text{J} \))

Q5. A metal has a threshold frequency of \( 4.8 \times 10^{14} \, \text{Hz} \). What is the kinetic energy of an electron ejected by light of frequency \( 7.2 \times 10^{14} \, \text{Hz} \)? (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q6. The angular momentum of an electron in the fifth Bohr orbit is: (\( h = 6.626 \times 10^{-34} \, \text{J s} \))

Q8. An electron in a hydrogen atom transitions from \( n = 3 \) to \( n = 2 \). What is the wavenumber of the emitted light? (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \))

Q9. The energy of an electron in the second orbit of \( \text{Be}^{3+} \) is \( -19.36 \, \text{eV} \). What is the ionization energy from the fifth orbit? (\( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

Q10. Which of the following transitions in a hydrogen atom emits light of the longest wavelength?